Personally, my favorite algorithms/data structures books is Algorithms 4th ed by Sedgwick and Wayne. It does a great job explaining the material from a theoretical standpoint, but also focuses on practical application in addressing real problems, and every algorithm comes with real, working Java code that in some cases is even superior to the implementations in the standard Java libraries.
And it perfectly accompanies Sedgwick's free algorithms course on Coursera.
I saw that he mentioned that he got the book off of an author's website for free and went looking for it -- found Dr. Vazirani's site and course page[0]. He mentions that it's available for download because at the time of writing, it wasn't found in bookstores.
Berkeley, in the meantime, has deliberately blocked access to the linked algorithms.html[1], as well as the root directory of the algorithm PDF files, suggesting to me that this is not an actual "free" book.
If anyone knows otherwise, I'd love to hear about it since I love free books.
Unlike TAOCP and CLRS it's actually readable in realistic amount of time.
This book is also very good at explaining theoretical computer science. In particular - NP completeness.
Official copy is available at home page of Umesh Vazirani at berkeley.edu:
0: Prologue - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap0....
1: Algorithms with numbers - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap1....
2: Divide-and-conquer algorithms - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap2....
3: Decompositions of graphs - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap3....
4: Paths in graphs - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap4....
5: Greedy algorithms - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap5....
6: Dynamic programming - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap6....
7: Linear programming and reductions - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap7....
8: NP-complete problems - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap8....
9: Coping with NP-completeness - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap9....
10: Quantum algorithms - https://people.eecs.berkeley.edu/~vazirani/algorithms/chap10...