Note: please edit this answer and add to it, do not create new answers
Rigorous books:
The artArt of computer programming by KnuthComputer Programming by Knuth
A discipleDiscipline of programming by DijkstraProgramming by Dijkstra
Introduction to Algorithms by Cormen, Leiserson, and Rivest by Cormen, Leiserson, Rivest, and Stein
Algorithms by Sedgewick and Wayne by Sedgewick and Wayne
Dr Dobb's Essential Books on Algorithms and Data Structures
This also includes introduction to algorithms
Algorithms + Data Structures = Programs by Wirth by Wirth and its followup:
Algorithms and Data Structures
The Science of Programming by Gries andby Gries and
A Logical Approach to Discrete Math by Gries by the same author
Algorithms on Strings, Trees and Sequences by Gusfield by Gusfield
Concrete Mathematics: A Foundation for Computer Science by Graham, Knuth and Patashnik by Graham, Knuth, and Patashnik
[The Theory of Parsing, Translation, and Compiling] The Theory of Parsing, Translation, and Compiling (part I and II)12
(part I and II) by Aho and Ullman
The Design and Analysis of Computer Algorithms both by Aho. Aho, Hopcroft, and Ullman
Introduction to Automata Theory, Languages and Computation by Hopcroft by Hopcroft and Ullman
Obviously the list can be extended quite a bit.
Note that as the field of computer science has expanded, books are unable to keep up and thus you'll have to turn to research papers.
