Hey Roberto,
I shall provide you an explanation over the usage of these words:
1) ''After'': It is usually a preposition. If something happens ''after'' a particular time or event, it happens during the period that follows that time or event.
E.g.: ''We'll hear about everything after dinner.''
*** You can say that someone does something ''after'' doing something else.
E.g.: ''After leaving school he worked as an accountant.''
E.g.: ''After completing and signing the form, please return it to me.''
2) ''Afterwards'': It is an adverb. If something happens ''afterwards'', it happens after a particular event or time that has already been mentioned. You often use ''afterwards'' in expressions like ''not long afterwards'', ''soon afterwards'', and ''shortly afterwards.''
E.g.: ''She died soon afterwards.''
E.g.: ''Shortly afterwards her marriage broke up.''
3) ''Afterward'' is also sometimes used, especially in American English.
E.g.: ''I left soon afterward.''
E.g.: ''Not long afterward, he made a trip from L.A. to San Jose.''
*** NOTICE: You can use ''after'', ''afterwards'', or ''later'' following a phrase that mentions a period of time, in order to say when something happens.
E.g.: ''I met him five years after his wife's death.''
E.g.: ''She wrote about it six years afterwards.''
E.g.: ''Ten minutes later he left the house.''
Hope that helps!!!