Reading Algorithms book, need to grasp the concept of a hashtable. They write about hashing with separate chaining and hashing with linear probing. I guess Java's HashMap is a hashtable, therefore I'm wondering what mechanism does HashMap use (chaining or probing)?
I need to implement simplest HashMap with get, put, remove. Could you point me at the good material to read that?
When the unique keys used for the Map are custom objects, we need to implement hashCode() function inside the corresponding type. Did I get it right or when is hashCode() needed?
Unfortunately the book does not answer all questions, even though I understand that for many of you these questions are low level.

hashCode()method, but for most purposes, your assesment in #3 is correct.