The aim of this thesis is to study classes of central simple algebras related to the two invariants: cohomological invariants and a numerical invariant, essential dimension. For every integer n ≥ 1 and a divisor m of n, we let Alg _n,m be the set of isomorphism classes of central simple algebras of degree n and exponent dividing m.

First, let F be a field of char(F) ≠ 2 and −1 ∈ F^×2 and H(F) be the Galois cohomology with the coefficient [special characters omitted]. We prove that the group of invariants of Alg ₄ is a free H(F)-module with basis {1, e₂, e₄}, which is due to M. Rost. For all 1 ≤ k ≤ 3, we also show that the group of invariants of Alg[special characters omitted] is a free H(F)-module with basis {1, γ₁, ···, γ_k}. Moreover, we prove that the value of the reduced trace form of cohomological invariants e_2k coincides with the value of γ_k.

Secondly, we find upper and lower bounds for the essential dimension of Alg_n,m. In particular, we show that ed(Alg_8,2) = ed₂( Alg_8,2) = 8 and ed_p( Alg[special characters omitted]) = p² + p for p odd prime.