Cluster characteristics of the 3D Lennard-Jones, LJ, fluid are determined by Metropolis Monte Carlo computer simulations. The percolation probability and cluster distribution is calculated for several state points in the gas-liquid equilibrium region of the LJ fluid. The cluster number distribution is used to analyze the distribution of clusters above and below the percolation threshold. Using scaling theory, the critical exponent, Ï , is determined from the cluster distributions. Deviation from the scaling law is evaluated using a modified scaling law that includes a surface term. It is found that the surface term is unnecessary in the gas-like area of the phase diagram. The density profiles of large non-percolating clusters are calculated in order to study the surface structure of the clusters. The coordination number within a cluster is calculated directly in the simulation and, with the cluster energy, is used to discern the amount of "liquid-like" structure of the cluster. The radius of gyration, R g, as a function of cluster size determines the fractal dimension, D f of the non-percolating and clusters above and below the percolation threshold density. Finite size effects are briefly studied and presented for a few of points. / Master of Science