No, Esperanto doesn't have contractions in the way they are used in English. The same can be said for many languages, actually. See the other answers for alternative ways of shortening the words.

A little bit of off-topic about formality: This only looks too formal to you because you are thinking in terms of English. Again, many languages don't have this shortenings as English does and to make something formal, you have to use diffrent words, pronouns, inflections (there are many examples: Spanish (tu/Usted), German, Russian, Bulgarian,…). As I remember reading somewhere, Zamenhof specifically wanted that Esperanto doesn't have formal pronouns or whatever means to differentiate between formal/informal. Maybe because the users of the language are supposed to feel like friends, or maybe for another reason. But that's the fact.

No, Esperanto doesn't have contractions in the way they are used in English. The same can be said for many languages, actually. See the other answers for alternative ways of shortening words.

A little bit of off-topic about formality: This only looks too formal to you because you are thinking in terms of English. Again, many languages don't have this shortenings as English does and to make something formal, you have to use different words, pronouns, inflections (there are many examples: Spanish (tu/Usted), German, Russian, Bulgarian,…). As I remember reading somewhere, Zamenhof specifically didn't want Esperanto to have formal pronouns or whatever means to differentiate between formal/informal. Maybe because the users of the language are supposed to feel like friends, or maybe for another reason. But that's the fact.