He has narcissistic personality disorder, here is the Mayo Clinics definition of the symptoms of this disorder;
"Signs and symptoms of narcissistic personality disorder and the severity of symptoms vary. People with the disorder can:
•Have an exaggerated sense of self-importance
•Have a sense of entitlement and require constant, excessive admiration
•Expect to be recognized as superior even without achievements that warrant it
•Exaggerate achievements and talents
•Be preoccupied with fantasies about success, power, brilliance, beauty or the perfect mate
•Believe they are superior and can only associate with equally special people
•Monopolize conversations and belittle or look down on people they perceive as inferior
•Expect special favors and unquestioning compliance with their expectations
•Take advantage of others to get what they want
•Have an inability or unwillingness to recognize the needs and feelings of others
•Be envious of others and believe others envy them
•Behave in an arrogant or haughty manner, coming across as conceited, boastful and pretentious
•Insist on having the best of everything — for instance, the best car or office"
I think it is not unreasonable to say Trump has the full set.