Explain the internal working of Java's Garbage Collector (GC). How does it optimize memory management? Discuss different GC algorithms and their trade-offs.

Java's Garbage Collector automatically handles memory management by disposing of objects that are no longer in use, preventing memory leaks. It has several algorithms, including Mark and Sweep, Generational GC, and G1 GC. Mark and Sweep is simple but can cause fragmentation. Generational GC optimizes by separating new and old objects, while G1 GC offers lower pause times but with higher complexity.