It's just that, an Alpha. Alpha stands for the first version of the game, which is riddled with bugs and glitches, and in the earliest form of production. As time goes on, and it advances to Beta and Gamma versions, it will become less buggy, it won't crash as often, and there will be more features. Just stick it out, and things will get better.
That or check your computer, or lower the game quality... that might work to.
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Either you have installed two mods incompatible with each other or installed something wrong or are even missing a file or two from the download if you may have installed only part of it. Go to the Minecraft launcher and then hit options and force update, log in and it should refresh you're bin but it will uninstall all mods and/or texture packs maybe.
If you tried to modify the minecraft.jar file, it might not work, and it will crash because the necessary files are damaged or missing. try either re-downloading the program or deleting the minecraft.jar so it re-downloads. the minecraft.jar is located under %appdata%.
You could be on a Google meeting whilst presenting your screen, and playing Minecraft.
One of the Minecraft files that are required to start it may be corrupted. Uninstall and reinstall Minecraft and see if that fixes it.
Do you have mods if so you must have installed them wrong or some mods are incompatible with each other.