Before you mark this is a duplicate, let me explain why this is different. Most of the books on algorithms are more of a reference. You basically have a list of algorithms at your disposal. But what happens when you need to create a new algorithm for something? These books don't teach how to think in terms of algorithms. So I'm looking for books that will teach me the thinking-process of creating algorithms. Any good suggestions?
My way favorite book along these lines is Udi Manber's Introduction to Algorithms: a creative approach. Of course I'm biased, since Udi's now a VP at Google, where I work, but I loved the book even when he was at competitors;-). Dated, but always in print and in fact in stock at Amazon, the book is exactly what you're looking for -- it teaches the way to think to create algorithms!
It uses a pseudo-language that's close to Pascal (the favorite teaching language at the time it was written) but in fact about as close to Python (which hadn't even been invented back then;-). And, mostly, it uses clear, sharp, concise, wonderfully written English -- just like any (English-language;-) book should.
Elements of Programming by Alexander Stepanov is amazing, but not an easy read.
Programming Pearls by Jon Bentley (2nd ed.) - this should be in every serious programmer's "top 10" books list.
I always recommend "Artificial Intelligence: A Modern Approach" by Russel and Norvig as a good way to learn programming and (non-traditional) algorithms.
"The Algorithm Design Manual" by Steven Skiena. I couldn't stop thinking in algorithms about everything for a few months after reading it. I even invented a new algorithm myself, although later it occurred to be "quickselect"...