Advice on economical transportation between the Algarve and Barcelona

I rented a place in Carvoeiro, Portugal, from mid February to mid
March, 2005.


During the 4 weeks I plan to tour the Algarve, and visit Lisbon and
Sintra.


I would also like to visit the following sites in Spain: Sevilla,
Granada, and Barcelona. I realize that Barcelona is far from the
Algarve.

I have rented a car for part of my stay.


I am not knowledgeable about travelling in Portugal and Spain.


I am seeking advice on alternative means of transport (other than

automobile) to the sites in Spain, particularly to Barcelona.


There does not seem to be direct rail connections between the Algarve
and Barcelona along the coast.


Any suggestions for a relatively inexpensive itinerary?


For example,


1) drive (or go by bus or train) to Lisbon then fly or take a train to

Barcelona?.


2) drive from the Algarve to Sevilla and Granada, leave the car in
Granada, and take a train or fly to Barcelona.

Would it be very expensive to park a car in a secure parking lot in
Lisbon,

or Granada or other city.?

Any advice would be appreciated.
Thank you.

(Thank you Nige for your reply to a previous posting)