Here is an incomplete list of math journals. Click the journal to visit its website. The list is not in any particular order and will be updated in the future. 

A. Comprehensive Journals

1. Annals of Mathematics 

2. Acta Mathematica

3. Journal of the American Mathematical Society

4. Inventiones Mathematicae

5. Duke Mathematical Journal

6. Journal of the European Mathematical Society

7. Mathematische Annalen

8. Journal für die reine und angewandte Mathematik

9. Communications on Pure and Applied Mathematics

10. Advances in Mathemacis

11. American Journal of Mathematics

12. Proceedings of the London Mathematical Society
    

13. Transactions of the American Mathematical Society

14. Journal of the London Mathematical Society
    

15. International Mathematics Research Notices IMRN

16. Advances in Applied Mathematics

17. Science China Mathematics

18. Acta Mathematica Sinica English Series

19. Journal of the Australian Mathematical Society

20. Bulletin of the Australian Mathematical Society
    

B. Specialized Journals

1. Journal of Combinatorial Theory, Series A

2. Journal of Combinatorial Theory, Series B

3. Combinatorica

4. Annals of Combinatorics

5. Journal of Number Theory

6. International Journal of Number Theory

7. Acta Arithmetica

8. Ramanujan Journal

9. Discrete Mathematics

10. European Journal of Combinatorics

11. SIAM Journal on Discrete Mathematics

12. The Electronic Journal of Combinatorics

13. Journal of Algebra

14. Algebra & Number Theory
    

15. Journal of Mathematical Analysis and Applications

16. Integral Transforms and Special Functions

17. Research in Number Theory

18. Integers, Electronic Journal of Combinatorial Number Theory

19. Journal of Integer Sequences

20. Hardy-Ramanujan Journal