
begeistert
enthusiastic
Feeling and showing great joy, enthusiasm, or admiration for someone or something.
Die Kinder waren vom Ausflug in den Zoo total begeistert.
The children were totally enthusiastic about the trip to the zoo.
enthusiastic / thrilled
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enthusiastic
Feeling and showing great joy, enthusiasm, or admiration for someone or something.
Die Kinder waren vom Ausflug in den Zoo total begeistert.
The children were totally enthusiastic about the trip to the zoo.
'Begeistert' (enthusiastic) is the past participle of the verb 'begeistern' (to inspire/excite) and is used as an adjective. The word contains 'Geist' (spirit/mind): to enthuse someone literally means to fill their spirit with joy or enthusiasm.
Die inspirierende Rede hat das Publikum begeistert.
The inspiring speech enthused the audience.
To express what you are enthusiastic about, you use the prepositions 'von' with the dative or 'über' with the accusative. 'Von' often describes general admiration, while 'über' usually refers to a specific event or piece of news.
Ich bin begeistert von deiner neuen Frisur.
I am enthusiastic about your new hairstyle.
The feeling of enthusiasm is often strengthened with adverbs. Common combinations are 'total begeistert' (totally enthusiastic), 'völlig begeistert' (completely enthusiastic), or 'hellauf begeistert' (absolutely thrilled).
Nach dem Konzert waren die Fans hellauf begeistert.
After the concert, the fans were absolutely thrilled.
crazy
Both words express great joy or a strong liking for someone or something. “Verrückt nach” is a fixed colloquial expression used with “nach” and sounds especially intense, while “begeistert von” is more neutral and also works well in more matter-of-fact situations. The choice therefore mainly depends on the expression used and the tone.

Mia ist seit dem Konzert von dieser Sängerin begeistert.
Mia has been enthusiastic about this singer ever since the concert.
Mia ist seit dem Konzert verrückt nach dieser Sängerin.
Mia has been crazy about this singer ever since the concert.