The (أنا ذاهب) means I'm going right now or in the near future but (أنا أذهب) means I go to school not necessarily right now like saying: 1- I'm going to the university to get some paper. 2- I go to Newyork University. As for للجامعة well it means (to the university), but جامعة just means (University). So لل means (to). I hope that helped.

Well, basically ذاهب in term of form is not a verb, it's a subject form which means "the one who is going". In term of meaning it indicates to the future (I will go). However, أذهب is a present continuous form (I'm going now), and can also be a present simple (I go). As for لـ, the verb أذهب it's transitive, so there must be a preposition, and basically the correct one here is إلى not لـ, so it should be أنا ذاهب/أذهب إلى الجامعة, yet we sometimes don't follow this rule so we say أذهب للجامعة. If one says: ذاهب/أذهب لـ it would basically mean: to go for/ in order to...they can be now interchangeable but origionally the suitable one is إلى.

hallo, أنا ذاهب للجامعة means I am going to the univetsity ( that means that I am at the moment on my way to the uni) أنا أذهب للجامعة means I go to the university also we use ل as preposition it means (to) when we add ل to a word that starts with (ال) we remove (ا) so it becommes (لل)