The algebraic K-theory is a branch of algebra that associates to any ring with unit R a sequence of abelian groups called n-th K-groups of R. In 1970, Daniel Quillen gave a general definition of K-groups of any ring R using the +-construction of the classifying space BGL(R). On the other hand, if we consider a commutative ring R, we can define the Milnors K-groups, K^M_n (R), of R. Using the product of the Quillen and Milnors K-groups and their anti-commutative structure, we define a natural homomorphism t_n : K^M_n (R) → K_n(R): In this dissertation, we show that if R is a local ring with maximal ideal m such that R=m is infinite, then this map is an isomorphism for 0<= n<= 2. But in general t_n is not injective nor is surjective. For example when n = 3, we know that t₃ is not surjective and define the indecomposable part of K₃(R) as the group K^ind₃ (R) := coker (K^M₃ (R) → ^t₃ K₃(R)). Using some results about the homology of linear groups, in this dissertation we will prove the Bloch-Wigner exact sequence over infinite fields. This exact sequence gives us a precise description of the indecomposable part of the third K-group of an infinite field. THEOREM (Bloch-Wigner exact sequence). Let F be an infinite field and let p(F) be the pre-Bloch group of F, that is, the quotient group of the free abelian group generated by symbols [a], a ∈ F^× - [1}, by the subgroup generated by the elements of the form [a][b]+ b/a][ 1-a^-1/1-b^-1]+ [1-a/1-b] with a; b ∈ F^×, a =/ b. Then we have the exact sequence Tor^Z₁ (μ (F), μ (F)) ~ → K^ind₃ (F) → p(F) → (F^× ⊗ ZF^×)$sigma; → K₂(F) → 0 where (F^× ⊗ ZF^×)σ := (F^× ⊗ ZF^×) / a &38855; b +b ⊗ a | a; b ∈ F^× and Tor^Z₁(μ(F);μ(F)) is the unique non trivial extension of Z=2Z by Tor^Z₁ (μ (F); μ (F)) if char(F) =/ 2 and μ₂ ∞ is finite and is Tor^Z₁ (μ (F);μ (F)) otherwise. The homomorphism p(F) → (F^×ZF^×)%sigma; is defined by [a] → a ⊗ (1-a). As it is shown, the study of the Bloch-Wigner exact sequence is also justified by the relation between the second and third K-group of a field F.