In reply to Alan M:
For alpine type ridges try Los Raspones, NW ridge of Cerro de Cartujo, NE ridge of Mulhacén, traverse of Puntal de la Caldera or the ridge between Cerro de los Machos to Veleta (finish up summer VD Fidel Ferero to summit).
For easier gullies the east side Raspones provides quite good sport and is close to the guarded Refugio Poqueira
Classic snow climbs on the north side (all at alpine AD/AD+) are
Canuto de Veleta
Espolon de Puntal de la Caldera
North canuto of Cerro de los Machos
NE ridge of Cerro de los Machos
Mulhacen N face - long routes and lots here but needs to be in good condition
Espolon de Alcazaba - a classic but is remote (reached from Güejar Sierra)
There is lots more but most routes will require use of unmanned refuges/bivvy. If you want more info about specific climbs then mail me. Happy to help.