There are various types of trees I know. For example, binary trees can be classified as binary search trees, two trees, etc.

Can anyone give me a complete classification of all the trees in computer science?

Please provide me with reliable references or web links.

It's virtually impossible to answer this question since there are essentially arbitrarily many different ways of using trees. The issue is that a tree is a structure - it's a way of showing how various pieces of data are linked to one another - and what you're asking for is every possible way of interpreting the meaning of that structure. This would be similar, for example, to asking for all uses of calculus in engineering; calculus is a tool with which you can solve an enormous class of problems, but there's no concise way to explain all possible uses of the integral because in each application it is used a different way.

In the case of trees, I've found that there are thousands of research papers describing different tree structures and ways of using trees to solve problems. They arise in string processing, genomics, computational geometry, theory of computation, artificial intelligence, optimization, operating systems, networking, compilers, and a whole host of other areas. In each of these domains they're used to encode specific structures that are domain-specific and difficult to understand without specialized knowledge of the field. No one reference can cover all these ares in any reasonable depth.

In short, you seem to already know the structure of a tree, and this general notion is transferrable to any of the above domains. But to try to learn every possible way of using this structure or all its applications would be a Herculean undertaking that no one, not even the legendary Don Knuth, could ever hope to achieve in a lifetime.