How much knowledge of maths is required for learning Lagrangian mechanics? Also from where can I learn this math?
In the UK, Lagrangian mechanics would normally be taught to first or second year undergraduate students who have a solid understanding of Newtonian dynamics and calculus with multiple variables. For an idea of the kind of texts you might need you could look at university syllabuses such as:
University of Manchester: http://bluebook.physics.manchester.ac.uk/10_syllabuses/physics_level1/phys_10101.html
University of Bristol: http://www.maths.bris.ac.uk/study/undergrad/current_units/unit/?id=140
which also give you an idea of the prerequisites.
If you do not yet master calculus, I recommend the book
Zeldovich Ya.B., Yaglom I.M.: Higher Math for Beginners, Mir 1988
which is great. Then, you need to understand
1) ordinary differential equations of 1st and 2nd order and have some idea about
2) many-variable calculus and
3) linear operators and matrices.
If you want to understand Hamilton's principle and its connection to Lagrangian mechanics, also calculus of variations, but you can learn that later.
For first encounter, you do not need things such as complex analysis, method of series (of any kind), partial differential equations or differential geometry.
You can learn the mentioned parts from introductory math textbooks for university students. For differential equations, the book
Sokolnikoff, I.S, Sokolnikoff E.S., Higher Mathematics for Engineers and Physicists, McGraw-Hill, 1941
from sec. 67 on seems quite nice.
These lecture notes by Stone and Goldbart may help for diff. equations (there is also some note on Lagrangian mechanics), matrices and calculus of variations:
(there is also a book).
I encourage you to search for the above topics in as many texts as you can get your hands on, in library and on the especially the Internet and stick with those few that seem best to you (concise but rigorous and well-explanatory).