Never use the word "gonna" someone who uses "gonna" shows signs of very poor English! "I am going to listen to the professor." this sentence is correct....

Gonna equals to going to, correct. And must be: going to + do something. So, the "go" after "gonna" is equal to that "do" >>> gonna go... Go listen, simply means go to do something, "去做某事", not go "and" listen, they're not in a relation of "and" but "to"; some scholars insist on the viewpoint that "go do something" (去做某事) is short for "go to do something", which means the "to" in the middle is just grammatically left out. While some think it's appeared as a fixed phrase: go do something. Go ask your teacher! Go fix it! Go scr** yourself! Go get it! It's spoken with somewhat an imperatival tone; or a future tense, indicates one's willing to be going to do something, eg: I'll go get it. I'm going to go play some WOW. I plan to go visit you. ... ... ...

Norman is correct that using "gonna" makes a person sound a bit lazy and perhaps uneducated. But, lots of English speaker's talk like that, so it is useful for foreigners to understand it. The sentence "I'm gonna go listen to the professor" means "I am going to go to listen to the professor" which is the same as "I will go to listen to the teacher". Here "going" means something like "planning" or "intending". For example: "I am going to learn Chinese" means "I intend to learn Chinese". Also note: "Go" means "go", in other words: to move in a direction away from the speaker. And "listen" really means "listen", as in: pay close attention to the sounds the teacher is making. In Chinese I believe this sentence is translated as "我要去听教授讲课".

gonna means going to so : i'm gonna listen to the profeesor i'm gonna go to listen to the professor we say: i'm going to travel to london; or i'm gonna travel to london i use gonna in informal speech neither in formal one nor in writing i never use gonna go listen