Maestro Alvarez trajectory begins in 1965 when he enrolls in the National School of Music at the National University of Mexico (UNAM). While studying there he earns a bachelor of Concert Accordionist. In 1976 he graduates with honours from the National Conservatory of Music where he earns a Bachelor of Concert Violinist and a Bachelor of Orchestral Conducting, all while the tutelage of Robert Vaska, Francisco Savin and Efrem Kurtz.

During this time he founds the  Conservatorys´ Choral Society, which, on several occasions, performs with the most renowned orchestras in Mexico, as well as the chorus "Axis Mundi". During this time he was the concertmaster of both symphony and chamber orchestras of the conservatory, first violin of the conservatorys´ quartet,  and winner of the scholarship that the Secretary of Public Education granted, in the orchestral conducting field,  during six consecutive  years.          

In 1974 he founds his first orchestra, the chamber orchestra of the "CENETI", conformed by the most prominent students from the Conservatory.

In 1976 he is appointed as a violinist in the UNAM Philarmonic.

During the  course of the years 1977 to 1980, maestro Alvarez acted as general coordinator of the tours that the following orchestras  gave through our country: Brooklyn Philharmonic, Dallas Symphony, Atlanta Virtuosi, Atlanta  Symphony, Louisville Symphony, and the Scottish Chamber Orchestra.

As a soloist, his participation as accordionist with the UNAM Philharmonic Orchestra is particularly noteworthy.

In 1980 he es invited to join the Mexico City Philharmonic Orchestra, as co-principal violin, where he remains until 1985,  being conducted by  some of the greatests batons: Leonard Bernstein, Efrem Kurtz, Isaac Karabachevsky, Emil Tchajarov, and accompanying soloists like: Ruggiero Ricci, Isaac Stern, Henry Szeryng, Guadalupe Parrondo.

In 1982 maestro Alvarez is distinguished as the first latinamerican to win a further training course in conducting scholarship from the Accademia Musicale Chigiana in Siena, Italy. There, he works with the eminent maestro Franco Ferrara.  At the end of the course he is chosen to conduct the Sophia Philharmonic Orchestra, accompanying pianist Stefan Ragni, for the graduation concert.

Maestro Alvarez earns an honourable mention granted by Leonid Kogan, Franco Gulli, Severino Gazzeloni, Ruggiero Ricci and Riccardo Muti, members of the jury panel. In 1983, upon his return to Mexico, he is named Assistant Conductor of the Mexico City Philharmonic Orchestra. 

In 1987 he founds the Philharmonic Society of Concerts the first private orchestra in Mexico-  where he is the artistic director, with which he performs seven seasons, innumerables private concerts, many world premiers, extended tours throughout Mexico, as well as the recording and digital editing of 25 albums, It is noteworthy to mention that the Philharmonic Society of Concerts  was a ground  breaking  orchestra in  Latin America. It was the first privately owned orchestra in the history of Mexico and Latin America;  it recorded more albums than any other orchestra and it was the first one to use digital editing. Furthermore, it had great acceptance among the general public.   The orchestra also premiered symphonic works by mexican composers.  One of maestro Alvarez greatest achievements with the Philharmonic Society of Concerts is that the repertoire included a medley of mexican music. He has elevated popular mexican music to the symphonic genre, a feat never previously achieved.  He also had, during more than two years, an exclusive broadcast devoted to his recordings.  

Maestro Alvarez also performed a very important role as a violin professor at the "Escuela de Iniciacion" and "Escuela de Perfeccionamiento", both part of the Conjunto Cultural Ollin Yoliztli (CCOY) in Mexico city. His students have obtained important awards in various national contests. As well, in 1992, with the collaboration of his most outstanding students, he founds the Chamber Orchestra of the CCOY, reaching a professional level.  In 1994, the Government of Mexico City awards him with the Medal of Merit for his outstanding contribution to the musical education of the mexican youth.

Maestro Alvarez has conducted numerous orchestras  including the Mexico City Philharmonic, Mexico National Symphony, UNAM's Philharmonic,  State of Mexico Symphony, Xalapa Symphony,  San Antonio Symphony,  Sofia Philharmonic, the National Symphony of El Salvador, the  Bellas Artes Chamber Orchestra, Hidalgo's University Symphony, Carlos Chavez Symphony and the Deutsche Kammerorchester among others.