Looks like a good book for your puzzle library.

https://www.kickstarter.com/projects/cubeindex/cube-index-a-visual-guide-to-mechanical-puzzles

Layer Merge by Lan Ho FREE

  

Layer Merge comes from Lan Ho. It's a very sophisticated and well polished stencil puzzle.

  

Each image shows a different problem.  Each one has 6 stencils.  The circle on the top left corresponds to the circle on the top right.  Both circles are controls.

The left control: rotates the stencil.
The right control: shift it up or down relative to the other controls to determine the stacking order.

According to Lan Ho, there are more than 100 puzzles.  That's probably too many by about 50. Why? Because these get really hard very quickly.  I was stuck on #6 before I realized that the right circles could move up and down. #7 is totally different from #6, but still quite hard. And that's where I stopped! At least for now.

Layer Merge requires concentration!

https://itunes.apple.com/us/app/layer-merge/id1196171842?mt=8

Other Stencil Puzzles:

Factory Balls Excellent
Art of Perception: Ravioli  Highly polished.
Motif Mask Kaleidoscope Puzzle

Switch It Puzzle by Krzysztof Topolski FREE

  

Switch It Puzzle comes from Krzysztof Topolski. It's a maze game with switches. The blue pieces fires a pulse in 1 direction.  Your task is to turn the other switches on/off in order to direct the beam to the yellow star. Some levels have a green tile. Which means that the pulse must pass through it before it gets to the yellow star.

  

Other levels require combining colors.
There are 51 levels. They go pretty fast. I've done 42 and will definitely finish them later today.  Hey, it's FREE.
https://itunes.apple.com/us/app/switch-it-puzzle/id1220478017?mt=8
https://play.google.com/store/apps/details?id=com.uglypixels.switchit

Pipe It by ANDREY NOVIKOV FREE

  

Pipe It comes from Andrey Novikov and Alexey Pajitnov, who is the author of the classic arcade game Tetris. The object is to place the pipe pieces in the grid so that every node gets lit. Also, all the pieces must be utilized.

  

There's a lot to like about Pipe It. First, when all the pieces are place the entire grid is not used. The graphics are good. I particularly like the levels that make you think there will be a symmetric diagram. Deceptive!

What could be better? Once you're stuck, it's impossible to see the outline of the individual pieces. So in effect, you have to move them all off the board.

There are 600 levels - way too many.  Also, in order to do the Normal levels, you have to first complete most of the 150 Easy levels.

There is something very relaxing about this puzzle. I did complete all the easy levels and moved on to the normal, hard and challenging levels.   At the moment I've solved 60 of the 150 challenging levels.
https://itunes.apple.com/us/app/pipe-it/id1198940085?mt=8

Omino! by Seth Caliskan Free

  

Omino! is a point scoring puzzle app game by Seth Caliskan. The object is to place the circles on the grid - carefully! - in order to get 3 of the same color in a row (horizontally or vertically). Key Point: some of the circles have an inner color. Look at the first image.  When that green circle is place, all 5 will disappear, but then that red inner circle will take over that cell.

 

Very Interesting: creating combos yield extra points. My largest combo was 4 strings. At the time, I thought: okay, there cannot be a combo bigger than 4.  But that's definitely wrong. I'm wondering what the longest combo was and who achieved it  That should be a Leaderboard category all by itself.

On the Leaderboard is the highest score.  Out of 1300 players, I'm #2.

One more thing: every 24 moves you make, you are given a gift. You can't always use the gifts right away.

Omino! is definitely a fun game. Graphics are perfect.  Give it a try. And if you beat my score, let me know.
https://itunes.apple.com/us/app/omino/id1196834851?mt=8

Other Point Scoring Games Worthy of Your Time
NumberMania
Four Straight Lines
Pushopolous
Stickets
Folt
Nineout
Nineout II
BeeCells Lite
Kindly Colors
HexAgony
Domino Drop
Put Number
Tripevo
Triple Town
Kindly  Colors
COLORswipe
SubaraCity
Virus Pop Smash
+1 Number
4 Way Puzzle
Merged!
Enso

Politaire

Treple

numDance

Black Boxes

o:anquan
Levels

Buckets

Hit N Run

Puppo!

Chinese-Puzzle by Yufeng Long FREE

  

Yufeng Long has produced a very mathematical puzzle game app called Chinese-Puzzle.  The object is to change the color of groups of circles so that all the circles will be the same.

  

There are 99 Yin levels and 99 Yang levels.
Without a doubt, they get pretty tough.  I did about 25 levels altogether.
I really like Yufeng's own description:
A CHINESE PUZZLE, A WORLD PROBLEM.
Last week, More than 130,000 Chinese testers, no one can solve the all levels.
Finalist of GMGC2016 Indie Pitch Arena.
.

I am a Chinese independent game developer, six months ago I designed a puzzle game "bdpq", fortunately it was featured by Apple in "Challenge Your Brain". This six months I have been thinking about how to design a new game that can go beyond it, more able to challenge the limits of human intelligence. After dozens of program attempts, I seem to find the way.

The source of Chinese civilization wisdom is Tai Chi of I Cing, it uses the most simple yin and yang conversion to explain the secret of all things change, thus affecting the Chinese civilization development for thousands of years. I have been thinking about how to make such a thought can be understood throughout the world as a simple game, so that everyone can experience this ancient wisdom, infinitely changing from simple changes

HOW TO PLAY

Swipe to select some dots.
Click the Tai Chi to change the color of the dots.
Change all dots to into the same color.

In the testing process we found that the Yang levels of the game is relatively simple, but the difficulty began to rise sharply in Yin leves, I even suspect that no one can solve the last level. Last week, More than 130,000 Chinese testers, no one can solve the all levels. So I made a "most expensive purchase" to remind you that it may be the world's most difficult puzzle, I hope you can solve it with your own brain.

Forgive my poor English :)

Sleeeeepfly Studios
Yufeng Long
https://itunes.apple.com/us/app/chinese-puzzle/id1157805434?mt=8

If you like Chinese-Puzzle, then you will certainly like the mechanical version known as Writer's Block from Oskar van Deventer. The object is to push the buttons using a certain key. The key pushes the buttons for 2 different groups of numbers.  Challenging.

  

http://www.passionforpuzzles.com/2013/11/writers-block.php

Plumber Connect: Hexa Puzzle by Le Oanh FREE

  

Plumber Connect: Hexa Puzzle comes from Le Oanh. I've done enough plumbing puzzles in the past. But this is the first one that has hexagonal cells. Unless I'm forgetting another one, which is quite possible.

There are 150 levels with triangle tiles, 150 with square tiles and 150 with hexagonal tiles.  Even the 'Hard' levels are easy.

There is another 'pipe' puzzle game that I've been doing.  I'll report on it within the next 2 weeks.

https://itunes.apple.com/us/app/plumber-connect-hexa-puzzle/id1223045440?mt=8

What's the name of this game? FREE

  

Puzzlers, I downloaded this game, but I don't know the title or the author. There is no menu, description or anything. Just the puzzles.

I downloaded this about 1 month ago.  The object is to roll the red cube, Your Man, and cover every square.  The orange squares are wormholes. The orange circle: landing on it will add new squares somewhere on the border.  Landing on the yellow circle: automatically blocks out squares so you don't have to land on.

There are 180 levels, I think. Of those, I've done about 100. It's not terribly hard. Also, the entire playing area takes up a tiny portion of the screen.

Sorry, no link. If you have played this game and can provide even a title, please do so in the comments.

Cosmic Hare by Simon Broggi FREE

Cosmic Hare comes from Simon Broggi. It's a peg jumping solitaire puzzle app game.

The object is to jump all the hares so that only 1 is left.

What's different:
1. The Red Eagle will swoop down, 1 cell at a time to devour a hare. Be careful.
2. Some levels show have a 3D element. (See last image.) That is, solve one face with 1 hare left, then rotate the shape, utilize that lone hare from the first face, to get the other faces.

What I really like: there are only 39 levels! I solved them all. I also like the intro graphics.

You know, I normally only mention the puzzle designer. Today, I'm listing the other people because it takes a team to make a good puzzle app.
Raffaele de Lauretis did Illustration.
Mark van Raai did Sound Design.
Ursina Wirz did Marketing, Communication.
Kai Jauslin did Original Light Installation.
https://itunes.apple.com/us/app/cosmic-hare/id1137163709?mt=8

Compel by Simon Eastwood Free

  

Simon Eastwood recently contacted me about his puzzle app game Compel. There are 3 games in one but they're very similar.

  

Let's start with the Classic version. Your task is to place a marker on every single cell, without dying. Look at the third image. The 4 in the top row is being tapped.  That means that the next move must take place on the bottom row.

You die by getting exactly 3 tapped tiles in a row.

I solved the 4x4 and 5x5 grids quickly. Though I did die a few times.  The 6x6 was hard! I needed about 10 attempts to solve it.  According to Simon, each time you load the game, a new level is generated.  According to him, there is not just one correct sequence.

Some puzzlers might classify this as a maze, where you must determine the starting and end points.

The second game is Checkers. The first piece you place will be white, then black, then white.... You will die if there are 3 whites or 3 blacks in a row. I solved the 4x4 & 5x5 levels.  6x6 is tough!

Compel is they type of puzzle app game that you must play carefully!  Moving too quickly will lead to trouble. I say this from much experience.

In the two versions I played, I came up with a specific strategy. But I'm wondering: would another strategy also work?  Simon: good job! I like the graphics too.
https://itunes.apple.com/us/app/compel/id1212468565?mt=8
https://play.google.com/store/apps/details?id=com.compel.compel&hl=en_GB

Plus Fifteen by Robert Currie FREE

  

Plus Fifteen comes from Robert Currie.  The object is to link up numbers that add up to 15.

  

Each level has exactly 1 solution. Grid sizes go from 6x6 to 9x9.

I like the graphics a lot.  For some reason, you can't redo a level that's already been solved.  Hmmm.

The fact that there is only 1 solution for each level leads to some interesting analysis.  Look at the first image. The top row has 11 & 4 directly in the center. Under it is 4 & 11.  If the top 11 pairs with the 4 below it or to its right, then the other 11 must pair with the 4 that's left or above it.  But because there's only 1 solution, we know that those pairings would lead to two possible solutions.  Therefore, that top 11 must pair with the 4 on its left.

https://itunes.apple.com/us/app/plus-fifteen/id1116789526?mt=8
https://www.facebook.com/plus15game

Blyss by Dropout Games FREE

  

Blyss is listed as an Editor's Choice by the Benevolent Powers of the App Store. Unquestionably the graphics are sweet and charming.  The game concept is unique too.

  

The object is to swipe adjacent tiles in groups of 3 or 4 and eliminate all the dots.

I solved 16 levels without failing. Then it sent me back to level 1 or its equivalent.

Blyss is going to be very popular with people who don't normally play puzzles.
https://itunes.apple.com/us/app/blyss/id991563953?mt=8

KAMI 2 by State of Play Games

  

KAMI 2 is one of those lucky games that the Editors of the App Store have singled out. Which translates into millions of downloads.  To be sure, this game is highly polished with impeccable graphics. In terms of originality.....it's very similar to the game Flood-It! and a slew of others. See list below.

  

The object is to get the whole field to be a single color. If you tap on a red triangle to make it blue, it will change colors and then absorb the other blue shapes that are contiguous to it.

Once you've done 25, you get the idea and they go pretty fast. However, some are definitely tricky.

There are 114 levels and I've solved 1 - 71.  Stuck on 72
https://itunes.apple.com/us/app/kami-2/id1133161444?mt=8

Similar Games
Coloruid
Colbox
Globs
Color Zen
Super Flood
Shapzzle
Color Contagious
Puralax

Rupiko by Niels Jansson FREE

  

Ruipiku comes from Niels Jansson. It's very much like his other game Shifty Bits, which I reviewed last year. The object is to slide the rows and columns so that the colors and shapes align correctly.

The concept is not new. I remember getting very tired of the concept about 4 years ago. But I like this. The graphics are nice.

The overall shape is rarely a rectangle.  I also like the black dots. When they appear, above a column, after your move you make, it pushes the column down one notch.

I did 31 levels. It's a fast game.  There are 100 levels.
https://itunes.apple.com/us/app/rupiku/id1170015153?mt=8
Not available on google play yet.

Loopine by Pyrosphere, Lda FREE

  

Loopine is a sweet little game that tests your timing/dexterity.  Each level has multiple shapes that intersect.  The bright line segments are constantly rotating around the perimeters.

    

Your task is to suspend the movement, then restart it so that there are no collisions with the segments from the other shapes.

There are 150 levels spread out over 3 levels of difficulty.  This is a very relaxing game.  Some of the shapes have a kind of Celtic knot look.
https://itunes.apple.com/us/app/loopine/id1205980465?mt=8
https://play.google.com/store/apps/details?id=net.pyrosphere.loopine