Lots are recommending CLRS, but IMO it is way too dry and dense for a first course.

I taught myself algorithms with the Algorithm Design Manual by Skiena, and I strongly recommend it. The first half is an exposition on algorithms, and it is mercifully readable, fun, and short. The second half is a catalog of different algorithms. You don’t really read through it, but it is useful as a reference if you have a specific problem you’re trying to solve and you want a background on algorithms in that area.