In this Ph.D. thesis we study a class of uniformly elliptic partial differential equations of second order in fully nonlinear nondivergence form with superlinear growth in the gradient and measurable coefficients. For equations with quadratic growth, we prove that multiplicity of solutions occurs when the operator is not coercive. We investigate the qualitative behavior of the continuums of solutions obtained for a parameterized family of problems. For this, we extend the Caffarelli-Swiech-Winter C1, alpha, regularity estimates to equations with at most quadratic gradient growth, showing that the solutions are continuously differentiable up to the boundary. Furthermore, we show a priori estimates in the uniform norm using purely nonlinear techniques in the nondivergence form, such as Harnack type inequalities and a Vázquez’s strong maximum principle for equations of our type.