Explain the internal workings of a Garbage Collector (GC) in Java. How does it manage memory and what are the different algorithms that can be used? How do they affect performance?

The Java Garbage Collector is responsible for automatic memory management. It tracks object references and identifies unused objects to reclaim memory. Some common algorithms include the Mark-and-Sweep algorithm, which marks reachable objects and sweeps away garbage, and generational collection, which segregates objects by age to optimize performance since most objects have a short lifespan. The choice of GC algorithm can significantly affect throughput and latency in applications, making understanding these tradeoffs crucial.