It is strange, but there are not so many historical sights in the capital of Spain, and the available ones are not as historical as I like :) - not older than XVI century. This is due to the fact that the intensive development of the city began only after 1561, when Philip II transferred the capital from Valladolid.
As for me, Madrid is primarily a transport hub. To Spain from Russia, direct flights can fly to only a few cities, but all of them, except Madrid are located on the coast, which is understandable. Connecting flights to other cities (usually through the Madrid) are more expensive than land transportation, and takes more time.
So, to begin with, check on thewebsite of Madrid airport whether there is a direct bus from the airport to the city you want (there is no direct train - the railway branch leads only to the capital). If not, you'll have to go through Madrid. How to use Spanish public transport I wrote in an article aboutSpain. With regard to the departure from Madrid, it means to determine the station from which we will go to their destination - there are a lot of them.
From Madrid airport you can get to the city by suburban train, metro or bus. In Spain the train is always more expensive, but, in this case, the most expensive mode of transport is the metro, because an airport fees added. In general, the difference in cost is only 2-3 euros, so that convenience comes to the fore, and the metro is often more convenient, since you can immediately get to the right place. A bus or a train takes you to the terminal station, where you still have to go to the subway. Of course, sometimes it happens that this particular terminal station is needed (for example, quite a lot of buses leave from Avenida de America station, where there is a direct bus from the airport).
So from cheap transport to expensive (prices at the time of writing the article - 2015):
1. City bus №101, to the metro station Canijahas (it's almost next to the airport) - 1.3 euros.
2. City bus №200, to Avenida de América - 1.3 euros. This is the metro station and bus station.
3. Suburban train to the station Príncipe Pío - 2.60 euros. There is also a metro and bus station. Stops: Chamartín - metro and railway station, Nuevos Ministerios - subway station, Atocha - metro and railway station, Méndez Álvaro - metro and bus station. Interval of movement - every half hour. The some planes arrive at Terminal 1, and the railway station is located near Terminal 4, between them about 5 km. You can go by a free bus, but it's again unnecessary traffic and time.
4. Metro - 4.50-5 euros, depending on the destination station.
5. Bus express №203, to the railway station and metro Atocha (Atocha) - 5 euros.
The Metro in Madrid is big, lots of people. Very long transitions at interchange stations.
Large transport hubs, where the metro and bus station are assembled, or even the railway station, occupy a large area - it can be difficult to navigate. Often, the terminals from where the buses go are located at the bottom, and the ticket offices on the other floor.
The same goes for the airport of Madrid (site of Barajas airport) - very long distances. From the moment the aircraft landed to its stop it takes about half an hour. Approximately the same time you need to go from the terminal to the metro.
Now about the sights of Madrid.
Madrid is located exactly in the center of the country. The geographical center of Madrid, and therefore of all Spain, is the Puerta del Sol (Gate of the Sun). Once there was a city wall, hence the name.
Gate of the Sun
Puerta del Sol
The Post Office at the Puerta del Sol
The main square of Madrid is called the Main square. :) The Plaza Mayor was built in the beginning of the XVII century. and served as a model for the numerous Plaza Mayor in other Spanish cities. It was really the main place of the city where all the most important events took place - from ceremonies with the participation of the king to the auto-da-fe and bullfight.
There are several churches and monasteries in the center, but they are not very interesting.
Church of St. Andrew
Real Iglesia de San Andres (XVII century)
Basilica of St. Mikhail
Basílica pontificia de San Miguel (XVIII century)
The main church of Madrid - Royal Cathedral of St. Maria Almudena is brand new. The Madrid diocese was established only in 1884 (before that Madrid belonged to the Toledo diocese), then the first stone was laid, and the construction was completed in 1993.
The Royal Cathedral of St. Maria Almudena
Catedral de Santa María La Real de La Almudena (XIX-XX century)
Nearby is the royal palace - a complex of buildings built in the mid-18th century. Large-scale construction. Now the royal family lives in another place, and in the palace they hold official events.
Palacio Real (XVIII century)
Palacio Real (XVIII century)
The Royal Palace and the Cathedraldral
Palacio Real y Catedral
The most unexpected sight of Madrid is the ancient Egyptian temple of Debod (4th century BC). It was transferred from Egypt, from a territory subject to flooding during the construction of the Aswan Dam and recreated in the West Park, near the Royal Palace.
Temple Debod in the West Park
Templo de Debod en Parque del Oeste
This, of course, not all sights, the city is large, some museums are worth.
There are a lot of tourists in the center of Madrid. Straight very, very. That's why I do not like the capitals - there is always crowded and all sorts of fuss.
Tourist map of the sights of the center of Madrid
The scheme of public transport of Madrid
The scheme of the Madrid Metro