Introduction to Algorithms by Cormen is a great. It is set up as a sort of reference and isnt necessarily meant to be read cover to cover. However, you'll need to read/understand the first 4 or so chapters (on asymptotic complexity, recursion, log rules, master theorem, ect) to really be able to grasp anything else in the book. The proofs and explanations can be rather terse, as it assumes you have some working knowledge with algorithmic theory and math. I wouldn't recommend it for starting out _at all_ as it can be very intimidating at first.
I started out with Algorithms by Tardos (you can pretty easily find a copy of the book and solutions online somewhere). It is less terse and goes through all the basics in a much less formal format. In this book I would advise starting at chapter 1 and going straight through to 8 or 9, doing the exercises and programming up most of the algorithms on your way. At this point you'll have a really nice working knowledge and can dive into Cormen and tackle stuff that interests you.
I started out with Algorithms by Tardos (you can pretty easily find a copy of the book and solutions online somewhere). It is less terse and goes through all the basics in a much less formal format. In this book I would advise starting at chapter 1 and going straight through to 8 or 9, doing the exercises and programming up most of the algorithms on your way. At this point you'll have a really nice working knowledge and can dive into Cormen and tackle stuff that interests you.