NotJumper

Based very heavily on Maddy Thorson's Jumper series, this game has been technically a project of mine since 2008 in one form or another. Which is not to say it is a grand adventure - rather it is a collection of precision platformer concepts that I desperately wanted to get into a reasonably playable form!
If you're familiar with the Jumper games you'll find that it borrows a lot of design elements and also the protagonist, but the level structures here can be a bit different.

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Instructions:

Use the arrow keys to move, and press Enter to select menu items and pause the game.
Your progress is saved at the beginning of each room.

Pressing Ctrl takes you to the level select, M will mute the music, and F4 will change the game from windowed to full-screen. If you need to, you can also press R to restart a level instantly.

There is also a classic cheat code you can enter anytime, which will unlock everything instantly or erase all progress (and you're not likely to enter it by accident, don't worry). Though it's not like you can't just edit the save file if you really want to anyway!

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Update 25/3/2018: 
-Changed a part of the World 7 special stage to be less difficult.

Update 1/4/2017:
-Removed the portals in special stages, as they're not generally necessary when you can just press Ctrl.
-Added an indicator on the level select to show which emeralds you haven't collected yet.
-Added an animation to the final level's red stuff.