During this first stage, the University of Oñati was just another Renaissance university, although without any State participation. While the building was being erected, somewhat by stealth (1543) - in order to avoid the jealousy of other universities and on the instructions of Mercado - classes began in the Casa de Hernani, as a private tutor's office.
The course opened in 1545 under the rectorship of the bachelor Pedro de Gorostarrazu and the teaching of the bachelors Lope de Burunsano and Gregorio de Mendizabal. Classes were given in the faculties of Theology, Institution, Canons, Law and Arts, following the model of the Colegio de San Bartolomé in Salamanca. Later, Medicine was added, graduating a large number of graduates who practised in the country, and which was suppressed by order of the Visitor Dr. Juárez in 1569.
The founder died in Valladolid in 1548, before he could leave his great work completely finished, but in the will that he granted again in the same city on 25th January of the same year he entrusted this care to his utors Miguel Muñoz, bishop of Cuenca and president of the Chancillería, and to the graduates Mercado de Peñalosa and Sancho López de Otalora. To this end, they were commissioned to draw up a volume of constitutions that would be more conducive to the better direction of the College, guided by those of the colleges of San Bartolomé de Salamanca and Santa Cruz de Valladolid. The following year the College presented the pontifical bulls of its erection to the Royal Council, and although this supreme court authorised their use, it was with the restriction that they had no effect in terms of secular jurisdiction, and that in everything else they should be governed as in the universities of Cuenca, Seville and Toledo. The testamentaries of Mercado, fulfilling on their part the latter's commission, ordered in the year 1552 a body of eighty-seven constitutions by which not only the College, but also the University incorporated into it, was governed, and they sent them to the rector and collegians for their punctual observance, as they promised under oath. These constitutions were reformed in the year 1569 by Doctor Hernado Juárez de Toledo, of the Royal Council, commissioned for this purpose by the King, as patron of the College. In the same order they were retouched in 1571 by the Royal Council, and in 1589 by Diego Arellano Zapata, doctoral canon of the Holy Church of Coria. In 1590 the Statutes were compiled and reformed.
The university student was subject to an almost monastic regulation, except in the case of living outside, in special inns, under close supervision. Despite these descriptions, there were, nevertheless, students with loud surnames, and there were known altercations and disturbances typical of the youthful condition of the collegiate students. A distinguished student during this period was the historian Garibay y Zamalloa. During these years it had three hundred students enrolled, which dropped to 200 in the middle of the 17th century. The number of professorships was also reduced: in 1606 there were three in Theology and four in Jurisprudence. In the middle of this century, Theology and Arts were also eliminated. In the second third of this century, the institution of the Colegio Menor de San Esteban in the University, with 4 professorships in charge of each Jesuit, which lasted until 1695, contributed to the economic support of this Institution, whose life was always very precarious. Particularly good were the relations with the University of Alcalá, with which admission to higher degrees without examination was practised.
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