'Despite' and 'in spite of' mean the same thing. But the most important difference is that when you use 'despite' you do not add 'of' to it and when you use 'in spite of' you have to use all 3 words 'in + spite + of.' For example: I failed the exam, despite the fact that I studied all week. I failed the exam, in spite of the fact that I studied all week. Both sentences are correct. But do NOT say: I failed the exam, despite of the fact that I studied all week. I failed the exam, in spite the fact that I studied all week. Both of these sentences are wrong.

The word 'despite' is not used with 'of' so you could say: Despite his fear of snakes, Tom agreed to hike in the woods for one hour. OR In spite of his fear of snakes, Tom agreed to hike in the woods for one hour. "Inspite" is not a word in the dictionary, therefore the word despite should always be used, and it means 'regardless of', or 'in defiance of' "In spite of" is a valid phrase, and has the same meaning as "despite," with the meaning given above "Despite of" is not grammatically correct.