The document discusses asymptotic notations used to analyze algorithms. It defines best case, average case, and worst case time complexities, and commonly used notations like Big-O, Big-Omega, and Big-Theta. Examples of common time complexities are given like constant, logarithmic, linear, quadratic, and exponential. Examples are provided for analyzing the time complexity of nested loops, matrix multiplication, and bubble sort algorithms. General rules for algorithm analysis are outlined regarding ignoring lower order terms and constants, summing segment times, and selecting the worst case complexity.