I am certainly sure that any one who has read Gil Kalai's witty community wiki has benefited a lot. Here I follow a similar track in asking this question. So let's compose a list of fundamental theorems in mathematics which may not even have the tag "fundamental" but have serious wight in the respective branch of math.

I will start with the elementary and very popular ones.(Please add a description if the theorem is fundamental but still not so well-known)

Thanks for all your effort.

FTA: The Fundamental Theorem of Arithmetic (or Unique-Prime-Factorization Theorem): ->Any integer greater than 1 can be written as a unique product (up to ordering of the factors) of prime numbers.

FTA: The Fundamental theorem of Algebra: -> The field of complex numbers is algebraically closed

FTC: The fundamental theorem of calculus: -> Has two parts and specifies the relationship between the two central operations of calculus: differentiation and integration.

FTLP: The fundamental theorem of linear programming: -> In a weak formulation, states that the maxima and minima of a linear function over a convex polygonal region occur at the region's corners.