I\'m looking for a clear, basic explanation of the concept of theta join in relational algebra and perhaps an example (using SQL perhaps) to illustrate its usage.
If I
You're not quite right - a theta join is a join which may include a condition other than = - in SQL, typically < or >= etc. See TechNet
As for cartesian product (or CROSS JOIN), it is an operation rather than an idea or concept. It's important because sometimes you need to use it! It is a basic fact that set of 13 x set of 4 = 52, and cartesian product is based on this fact.