Itinerary Suggestions

Use the Renfe site (www.renfe.com) to look at train times (AVE is the way to go between Madrid and Barcelona). Register with the site first, and it will be easier to use. You can change the site to English by clicking where it says "welcome" on the top right.

Here is an extensive tutorial on using the RENFE site: http://tinyurl.com/cu48wk5 Have you already booked your flights? If not, especially with only 9 days, you would do much better to fly into Barcelona and out of Granada. If you are locked into RT tickets to Madrid, you will lose a good part of your 9 days in transit (even though the trains from Barcelona to Madrid and Madrid to Seville are less than 3 hours, you have to add time getting to and from the stations). Even with open-jaw tickets, you'd be hard pressed to see 5 or 6 cities in 9 days; with round-trip tickets, I'd want to eliminate at least one place, to preserve my sanity.

I agree with other posters - you are trying to cover a lot of ground in 9 days. 9 days will be pushing it to just see Madrid, Granada and Sevilla with day trips to Cordoba and Toledo. My first trip to Spain (currently on third trip),we flew into Granada and out of Madrid - with a car between Granada and Sevilla so we could visit some of the Pueblos Blancos.
It was very hard for me to give up Barcelona the first trip, but I told myself I would return for Barcelona - and did.... Spain is really pretty big and if you spend so much time traveling large distances, you will miss the opportunity to slow down and enjoy this lovely country.

Your biggest obstacle is that you're hopscotching. Get a map and put dots on it, then connect the dots more logically. You've got time. Use Nancy's scoop for trains. Whichbudget or skyscanner for planes.