In this book, I present several research results accomplished under the supervision of Professor Yair Censor at the University of Haifa, Israel. Several iterative algorithms for solving the Variational Inequality Problem (VIP) in finite-dimensional Euclidean spaces are given. The main contribution is the development of a new algorithmic scheme for solving the VIP. This new algorithmic scheme includes as special cases some earlier algorithms for solving the VIP. Some of the results can also be found in: Y. Censor and A. Gibali, Projections onto super-half-spaces for monotone variational inequality problems in finite-dimensional spaces, Journal of Nonlinear and Convex Analysis (JNCA, Yokohama Publishers), 9 (2008), 461-475.