See the Sun Collections Framework overview, which includes an annotated outline and a tutorial path. See also the CFX examples. See also the MageLang Institute tutorial on the Collections Framework on Sun's site, to which there are links from the notes below.
Set theory gives us the mathematical concepts of a set being a unique collection of items, with no duplicates. This is often illustrated in a Venn diagram (taken from Sun's site) as:
where we can see intersections and unions of sets. Examples of sets are: the set of reserved words in Java, the set of nonnegative prime numbers. Sets contain only one instance of an item, sets may be finite or infinite, and sets can define abstract concepts.
A map is a special kind of set. It is a set of pairs with each pair representing a one-directional "mapping" from one element to another. Examples of maps are: map of IP addresses to domain names, map of keys to database records, map of conversions from base 2 to base 10.
The Collections framework is made up of a set of Java interfaces for working with groups of objects. The following image map diagram shows the hierarchy. Click inside the diagram on the class name for the API/tutorial documentation, or on the text inside the box for explanation and examples. You may also select the CFX text in the box for links to examples. CFX also has Iterators and common algorithms. You can also browse the directory of CFX examples. (All CFX shortcut links in the above paragraph currently don't work correctly in FireFox browsers.)
Note also the Array class, which is part of the Collections Framework, giving arrays with built-in sorting and searching.
See the lecture notes describing sequence of exploring the above diagram.
You may also work through some practical examples involving storing Student test scores, using the above classes, with corresponding examples lecture notes.
To easily use the Collections Framework, your classes should properly implement the following methods:
See this pdf document (username:password required) describing these methods.