I will be at a conference in Lisbon mid-May and want to travel 9 or 10 days afterwards within Portugal, including seeing Lisbon since I will not have time during the conference to see the city. I would like to visit the Algarve, Porto, Lisbon and Sintra. Can this be done within 9-10 days? How would you organize the itinerary considering that I will be starting from Lisbon? Thank you in advance to all of you experts out there!!

Add Evora and Coimbra on your way north to Porto.

All wonderful destinations, and we've seen them all in 4 weeks, so you need to be very selective. Algarve is way too far out, so it's the logical one to skip. Will you have a car after Lisbon? An idea of a very rushed itinerary, but doable if you don't mind the pace:
1, 2 - Lisbon - sleep in Lisbon
3 - Sintra - sleep in Lisbon
4 - Belem - sleep in Lisbon
5 - Evora - sleep in Lisbon
6 - Tomar - sleep in Tomar
7 - Alcobaca and Batalha - sleep in Tomar
8 - Coimbra - sleep in Porto
9,10 - Porto, fly out from there
Start early on the days you need to travel. We had a car, but I think all these towns are well connected by trains. You can join a tour for Alcobaca and Batalha, they are amazing. Have a wonderful trip!

as xyz99 has told you, skip the Algarve this time, as it's the outlier and too time to consuming to get down to and back in your short time frame.

Thank you so much, HappyTrvlr, xyz99 and Maribel, for your thoughts on this trip - I greatly appreciated it! Thanks, xyz99 for the detailed itinerary - it definitely looks doable.