A Phrase: A phrase does not contain either a subject (who or what the sentence is about) or verb (information about the subject) and, consequently, cannot convey a complete thought. A phrase contrasts with a clause. A clause contains both a subject and verb, and it can convey a complete idea.

 

An independent (or main) clause expresses a complete thought and can stand by itself as a sentence.

I went to the movies.

 

A dependent (or subordinate) clause does not express a complete thought and cannot stand alone as a sentence.

after I finished studying

 

Simple - one independant clause
Matthew took his umbrella.
We ate and slept in the same room. Compound Subject
The teacher spoke kindly but firmly. Compound Verb

 

Compound - two or more independant clauses joined together.
The thunder rolled; the lightening tore across the sky.
They rang the doorbell, but no one answered.
John has poor eyesight; therefore, the optometrist prescribed glasses. 

 

Complex - independant and dependant clauses joined together.
We took the wrong turn when we reached the place where the road divided.

If you buy a camera, do not choose one that is very complicated. 

If the dependent clause comes first, you need a comma. You don't need a comma if it comes after the independent clause. 

 

Compound-Complex 
Although he had many possessions, they did not satisfy him, and he longed for the happiness that others had.