In summary, the original titles and publishing dates of Padura’s book series featuring inspector Mario Conde are:
Pasado perfecto (EDUG, Dirección de Publicaciones, Universidad de Guadalajara, Mexico, 1991) (Ediciones Unión, La Habana 1995 and in 2005) (Tusquets Editores, 2000) English title Havana Blue (Bitter Lemon Press, 2007) Translated by Peter Bush.
Vientos de cuaresma (Ediciones Unión, La Habana, 1994) (Tusquets Editores, 2001) English title Havana Gold (Bitter Lemon Press, 2008) Translated by Peter Bush.
Máscaras (Unión de Escritores y Artistas de Cuba and Tusquets Editores, both editions in 1997) English title Havana Red (Bitter Lemon Press, 2005) Translated by Peter Bush.
Paisaje de otoño (Tusquets Editores, 1998) English title Havana Black (Bitter lemon Press, 2006) Translated by Peter Bush.
These four books make up the Havana Quartet (also known as The Four Seasons)
Adiós, Hemingway (Ediciones Unión, La Habana, 2001; together with the novella La cola de la serpiente, written in 1998) (Tusquets Editores published Adiós Hemingway in 2006) English title Adiós Hemingway (Cannongate Books Ltd, 2005) Translated by John King
La neblina del ayer, (Ediciones Unión, La Habana, 2005) (Tusquets Editores, 2009) English title Havana Fever (Bitter Lemon Press, 2009) Translated by Peter Bush.
La cola de la serpiente, revised version (Tusquets Editores, 2011)
Herejes, (Tusquets Editores, 2013)
A Crime is Afoot 
After reading this, I realize that I bought the third book in the series, not the first. Would it make any difference to read Havana Red first or better to start from the beginning?
I would suggest you read the one you have Tracy. Afterwards, if you find it of interest, you’ll have time for reading the other books in the series in order.
That sounds good. My husband thinks he might want to try this series too.