Günter is right. The verbs are completely different. "fangen" to catch, "anfangen" to begin. The verb "anfangen" is a separable verb (trennbares verb). try to look for a chapter in your book, that explains separable verbs. In general, when you learn the verbs, you will learn the infinitive of the verb "anfangen". The problem is, that as soon as you start to conjugate separable verbs you use there prefix (here "an") at the very end of the sentence. eg. "fangen" Ich fange den Ball mit der Hand. - I catch the ball with my hand. eg. "anfangen" Ich fange mit der Übung nach dem Essen an. I start with the exercise after the meal. See how in the second example the an moves all the way to the end of the sentence. We have many many verbs that work like this and it is important to understand how they work. otherwise you will be confused again and again. ziehen (to pull), einziehen (to move in) nehmen (to take), zunehmen (to gain weight) conjugated those verbs are - ich ziehe - or - ich ziehe ein. and - ich nehme - or - ich nehme ab. other prefix that are separable from the verb are - eg. ein..., aus..., auf..., ab..., mit...., vor...., zu..... again, you will come across lots of verbs that are separable and according to the prefix have different meanings. if you take for example the verb "kommen" (to come) you have ankommen (arrive). Ich komme am Bahnhof an. I arrive at the train station. auskommen (get along). I komme gut mit dir aus. I get along well with you. aufkommen (to appear). Das Gerücht kommt immer öfter auf. The rumour appears more and more often. umkommen (to die). Er kommt im Krieg um. He dies in the war. You see, how the separable prefix of a verb can have a drastic impact on the meaning of the verb - it basically is a different verb. if you ever get frustrated with German i suggest Mark Twain's essay "the aweful german language", where he very sarcastically speaks about, among other grammar topics, the separable verbs.

anfangen (begin) ; ich habe gestern mit dem Deutschkurs angefangen. fangen ( catch) : ich habe den Dieb gefangen.

Hi Leandro, these actually are two completely different verbs, one is "fangen" which basically means "to catch", the other is "anfangen" which means "to begin". The word "anfangen" is built with the prefix "an", which can, under certain circumstances like in this example, stand separately from the verb itself. The rest of the verb is used identically in both cases, so I guess that makes it quite hard. For the past tense (Perfekt), the difference is again clearer, as "I have begun" would be "Ich habe angefangen". Unfortunately I do not know, how or why these verbs developed linguistically in this way, maybe someone else can explain that better.