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In this work, we look into some results about dense subspaces of $C[0,1]$.Being our starting point the Weierstrass' Approximation Theorem, we studygeneralization of this in two directions: the first one studying subspaceswhich also have algebra structure, where the main result will be theStone-Weierstrass theorem, and the second one will be considering subspacesgenerated by sets of monomials whose exponents satisfy certain properties,where the central result will be the M\"untz-Sz\'asz theorem. Finally, wegather some of the most recent advances from this topic.

Subespacios densos de $C[0,1]$. Teoremas de Stone-Weierstrass y de M\"untz-Sz\'asz