Complex sentence: At that time he is invited to make part of the Madrid Contemporany Music Group directed by the Spanish composer Enrique X. Macias, having had the opportunity to take part in a series of shows both in Portugal and Spain.
Split into simpler sentences: At that time, he was invited to take part in the Madrid Contemporary Music Group, under the direction of Spanish composer Enrique X. Macias. This gave him the opportunity to take part in a series of shows both in Portugal and Spain.