Rigorous Books on Algorithms
Note: please edit this answer and add to it, do not create new answers

Rigorous books:

The Art of Computer Programming by Knuth  

A Discipline of Programming by Dijkstra

Introduction to Algorithms by  Cormen, Leiserson, Rivest, and Stein 

Algorithms 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 and its followup:
Algorithms and Data Structures  

The Science of Programming by Gries and
A Logical Approach to Discrete Math by the same author

Algorithms on Strings, Trees and Sequences by Gusfield

Concrete Mathematics: A Foundation for Computer Science by Graham, Knuth, and Patashnik

The Theory of Parsing, Translation, and Compiling (part I and II) by  Aho and Ullman

The Design and Analysis of Computer Algorithms by  Aho, Hopcroft, and Ullman

Introduction to Automata Theory, Languages and Computation 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.