To make this easier, we’re going to break all these words into two groups:

1. Despite and in spite of are prepositions, meaning that they must be followed by nouns or verbs in the gerund.

Despite having studied, Peter just couldn’t pass the exam.
Kelly couldn’t get into the disco in spite of knowing the disco’s owner.

2. Although, even though, and though are conjunctions, meaning that they are followed by conjugated verbs.  The first two start usually start clauses, while the last one usually ends them.

Although/Even though Peter had studied, he couldn’t pass the exam.
Peter couldn’t pass the exam, although/even though he had studied.
Kelly knew the owner of the disco.  She still couldn’t get into the club for free, though.

There are two things to be careful with:

First, despite is a one-word preposition; in spite of is a three-word preposition.  Despite of does not exist!

Secondly, the phrase “the fact that” after the prepositions turns them into conjunctions.  Basically, despite the fact that or in spite of the fact that are interchangeable with although or even though.

Danny got an A on the exam     even though he hadn’t even read the book!
although he hadn’t even read the book!
despite the fact that he hadn’t even read the book!
in spite of the fact that he hadn’t even read the book!

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