In 1880, Alcover received education from two professors of the seminary, Antoni Lladó and Pere Amengual. Surely, they were responsible for Alcover’s taste for geometry and exact sciences, especially regarding technical and artistic drawing. At the end of that year, he met Miquel Costa i Llobera, when he enrolled in Francesc Mestre’s academy of drawing and painting. Some of his drawings from his notebooks as well as some religious oil paintings and still lives are still preserved. Alcover’s drawings show high quality and, in particular, his technical sketches demonstrate a deep knowledge of lineal drawing and of the tools used in the design studios of his time.
When he travelled to Catalonia and the Pyrenees, he copied and drew many Romanic churches. He loved Romanic art and he applied his knowledge to the construction of different churches and temples. Probably, Alcover was influenced by the writings about art and architecture collected in several costumbrist journals, such as La Dulzaina and Revista Balear de literatura, ciencias y artes,in which there were publications by Miquel Ferrà, architecture and construction foreman, and Pere Alcàntara Penya, major construction foreman of fortifications. They both became friends, collaborators and teachers of Alcover in many aspects. Other influences can also be pointed out, for instance, the painter and art theorist Joan Oneill, friend with whom he shared Carlist ideology.
Alcover was interested in state-of-the-art architectonical techniques. There is evidence that he bought books by the French architect Éugene Viollet-le-Duc, who was very influential as an architectural theorist and building restorer at the turn of the 20th century.
Alcover participated in the construction and restoration of many buildings and monuments, the church and sacristy of Sant Miquel in Son Carrió (Sant Llorenç) being the first. He also reformed the chapel of Son Negre (Manacor), the church of Calonge (Santanyí), the Cathedral of Palma, the Chapel of the Holy Stone in Santa Ponça or the sepulchre of Ramon Llull in the church of Sant Francesc in Palma.