Question

Which field of mathematics should I study in order to familiarize myself better with Lagrange multipliers ?

Answer 1

Multivariable Calculus goes over this.
In Multivariable Calculus, Lagrange multipliers are used to find maxima and minima of a function subject to constraints.

Answer 2

I hope that helps.

Answer 3

Thank you AnimalLover8

Answer 4

No problem.

Answer 5

Lecture 13 is good
http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-13-lagrange-multipliers/

for background you may also want to see lecture 12, about gradients