With increasing traffic in near-Earth and Cislunar space, it has become essential to develop fast and accurate methods of predicting collisions between space objects. This is an important topic of discussion in current Space Situational Awareness (SSA) domain research. Orbit determination methods provide users with a state and an uncertainty associated with an object in space. This tells the user where the spacecraft is and with what percent certainty. Because there are limited observation resources, it is essential to have the ability to propagate this information to desired times accurately. Generally, this is accomplished using numerical Monte Carlo methods, where a point cloud of millions of points is taken from the initial uncertainty and each of these points are propagated to the final time. This is highly accurate with a large number of points but adds to a high computational expense. To minimize this cost, we look for analytical and semi-analytical methods that are faster but can still reach good statistical accuracy. This seminar will focus on an introduction to SSA, collision prediction methods, and the semi-analytical toolkits developed to achieve fast and accurate collision probabilities. The target audience is students and young professionals interested in SSA research and tools.