To play this game, use the patching program "Floating IPS" (flips) to patch the .bps file to a copy of "Super Mario World (USA).sfc". Then load the resulting file in the SNES emulator of your choice.

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Despite the difficulty of this game, it was designed to be beatable without in-deph knowledge of obscure techniques or glitches. The Training Room level is a place to practice the advanced "regrab jump" technique - if you're new and/or don't know what those are, it's a good place to train if you find yourself making no progress in the main game.

If you're -really- new, here are some basic Super Mario World mechanics:
-Mario jumps higher when he has more horizontal speed.
-Holding down to slide down slopes can give Mario more speed than he can attain by running.
-When underwater, you can hold up or down to swim higher or lower. You can even cut your momentum mid-swim by releasing up or pressing down.

If you're a seasoned player and want to know the list of physics changes that have been made from the original game, here they are:
-Wall clips are no longer possible
-Spinjumping on multiple overlapping enemies won't hurt you
-Throwing items up while spinning throws them over your center, instead of up from your hands in whichever direction you happened to be facing
-Jumping is no longer bugged when moving at extreme speeds, and holding run + forward in the air won't slow you down if you're going faster than normal moving speed, e.g. after jumping off a slope (this patch is "Player X Speed Fix 3.0" on smwcentral)
-Entity interaction is processed every frame. (The original game processes entity action every other frame, leading to inconsistent bounce heights.)

Good luck!