**Note: please edit this answer and add to it, do not create new answers**

Rigorous books:

[The art of computer programming by Knuth][1]  

[A disciple of programming by Dijkstra][2]

[Introduction to Algorithms by Cormen, Leiserson, and Rivest][3]   

[Algorithms by Sedgewick and Wayne][4]  

[Dr Dobb's Essential Books on Algorithms and Data Structures][5]  
This also includes `introduction to algorithms`  

[Algorithms + Data Structures = Programs by Wirth][6] and its followup:  
[Algorithms and Data Structures][7]  

[The Science of Programming by Gries][8]  and  
[A Logical Approach to Discrete Math by Gries][9]

[Algorithms on Strings, Trees and Sequences by Gusfield][10]    

[Concrete Mathematics: A Foundation for Computer Science by Graham, Knuth and Patashnik][11]  

[The Theory of Parsing, Translation, and Compiling (part I and II)][12]  
[The Design and Analysis of Computer Algorithms][13] both by Aho.

[Introduction to Automata Theory, Languages and Computation by Hopcroft][14]

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.  


  [1]: http://www-cs-faculty.stanford.edu/~uno/taocp.html
  [2]: http://www.amazon.com/Discipline-Programming-Edsger-W-Dijkstra/dp/013215871X
  [3]: https://mitpress.mit.edu/books/introduction-algorithms
  [4]: http://algs4.cs.princeton.edu/home/
  [5]: https://books.google.nl/books/about/Dr_Dobb_s_Essential_Books_on_Algorithms.html?id=XVJXmgEACAAJ&redir_esc=y
  [6]: http://www.amazon.com/Algorithms-Structures-Prentice-Hall-Automatic-Computation/dp/0130224189
  [7]: http://www.amazon.com/Algorithms-Data-Structures-Niklaus-Wirth/dp/0130220051/ref=pd_sim_14_5?ie=UTF8&dpID=51lEDsnLcWL&dpSrc=sims&preST=_AC_UL160_SR121%2C160_&refRID=0AR24W8J9PP90NANGPT2
  [8]: http://www.amazon.com/Science-Programming-Monographs-Computer/dp/038790641X/ref=pd_sim_14_4?ie=UTF8&dpID=41ttSkbcMQL&dpSrc=sims&preST=_AC_UL160_SR120%2C160_&refRID=0AR24W8J9PP90NANGPT2
  [9]: http://www.amazon.com/Logical-Approach-Discrete-Monographs-Computer/dp/0387941150/ref=pd_sim_14_1?ie=UTF8&dpID=412u0ErUXtL&dpSrc=sims&preST=_AC_UL160_SR97%2C160_&refRID=0TQBJX0HYPTDBZBNG48F
  [10]: http://www.amazon.com/Algorithms-Strings-Trees-Sequences-Computational/dp/0521585198
  [11]: http://www.amazon.com/Concrete-Mathematics-Foundation-Computer-Science/dp/0201558025/ref=pd_sim_14_22?ie=UTF8&dpID=61oqP3wQsiL&dpSrc=sims&preST=_AC_UL160_SR113%2C160_&refRID=0AR24W8J9PP90NANGPT2
  [12]: http://www.amazon.com/Theory-Parsing-Translation-Compiling/dp/0139145567/ref=pd_sim_14_30?ie=UTF8&dpID=411VqdgO9aL&dpSrc=sims&preST=_AC_UL160_SR110%2C160_&refRID=0AR24W8J9PP90NANGPT2
  [13]: http://www.amazon.com/Design-Analysis-Computer-Algorithms/dp/0201000296/ref=pd_sim_14_7?ie=UTF8&dpID=41XRY08FKHL&dpSrc=sims&preST=_AC_UL160_SR106%2C160_&refRID=1RS847M43Y1DDWQGMNRX
  [14]: http://www.amazon.com/Introduction-Automata-Languages-Computation-Addison-Wesley/dp/020102988X/ref=pd_sim_14_2?ie=UTF8&dpID=51NP7FFE1BL&dpSrc=sims&preST=_AC_UL160_SR107%2C160_&refRID=1C9A75P9086K8J67SVY1