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.

1. 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.
        
2. FTA: The Fundamental theorem of Algebra:
       -> The field of complex numbers is algebraically closed

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

4. 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.