Introduction to Algorithms (CLRS) by Cormen, Leiserson, Rivest, Stein (2022) — The reference algorithms textbook. Comprehensive and rigorous. (copyrighted)
The Algorithm Design Manual by Steven S. Skiena (2020) — Practical algorithm design with a war-stories approach. (copyrighted)
The Art of Computer Programming by Donald Knuth (1968–) — The Mount Everest of CS. Definitive but demanding. (copyrighted)
Algorithms by Jeff Erickson (2019) — Excellent algorithms text, free, covers the essentials beautifully. PDF
Introduction to the Theory of Computation by Michael Sipser (2012) — Automata, computability, complexity. The clearest treatment. (copyrighted)