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Initially named after its founder, Accademia Parassiana, it was dedicated to philosophical and literary studies. After Parassio’s death in 1543, Bernardino Telesio reorganized the academy, which was renamed Accademia Telesiana (Telesian Academy). A few years before Telesio’s death (in 1588) the Telesian Academy moved under the control of Sertorio Quattromani, who finally named it Accademia Cosentina.
Around 1593, following the conspiracy of Tommaso Campanella and Antonio Serra, who wanted to free Calabria from the Spanish viceroy system, the Academy was closed down. In 1608, however, the Church opened a new Academy, the Accademia dei Costanti, under the patronage of Constanzo[who?]. This new Academy was, in effect, the restoration of the Accademia Cosentina, but with the greater part of its members being from the Church. The Accademia dei Costanti continued under the guidance of Costanzo until his death in 1617.
Around 1649 Archbishop Giuseppe Sanfelice founded in Cosenza the Accademia dei Negligenti, which lasted until his death in 1660. In 1668 the Accademia dei Costanti became active again under the leadership of the poet Pirro Schettini until his death in 1678 . In 1756 Gaetano Greco revived the old Academy changing its name to Accademia dei Pescatori Cratilidi, but this attempt at revival lasted only until 1794. In 1811, the Academy was revived through the work of Matteo Galdi, and named the Istituto Cosentino. In late 1817, the King gave his approval for it to take once again the name Accademia Cosentina.
On 11 June 1871 the Cosentian Academy founded the Civic Library (Biblioteca Civica), which remained inactive until its officially inauguration on 4 March 1898.