Foundation: 1902-20
Though the Spanish league was still around the amateur level at the time, Madrid FC, called Madrid FC at the time, became of the top teams already for them and getting a strong fanbase at Madrid. They did win some trophies as well winning multiple Spanish Cup trophies.
National Recognition: 1920-40
Now called Real Madrid, they were one of the teams in the first Spanish Division One in 1929. A few years later winning leagues titles as well in 1932 and 1933. Though due to civil wars at the time this weakened the club ever so slightly.
The Bernabéu and Europe: 1940-60
Santiago Bernabéu became president in 1943 and opened their new stadium five years later. Real Madrid also signed one of the best players Alfredo Di Stéfano who became a legend at the club. They also won many European Cups between 1956 and 1960. This was one of the greatest teams in football history and this was due to their finances, recruitment and ambitions.
Success after golden era: 1960-80
Though real Madrid never reached the Di Stéfano years, they still won European Cups and Spanish titles. They were able to continue they strong success even after a golden era passing, many teams would see a drastic decline.
Academy and dominance: 1980-2000
Real Madrid ended an over 30 year drought of not winning the Champions League though winning consecutive league titles and multiple UEFA Cups. While dominating in leagues and cup success they also created a superb youth academy with players like Emilio Butragueño, Manolo Sanchís and many more.
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Though starting of a little off foot after a few years they started their dominance and with many Champions Leagues, many league titles to their name. They also have created a decorative youth academy and their player signings of Alfredo Di Stéfano and later on in the 2010s they would go on a similar run to the Alfredo Di Stéfano era with the line up of Gareth Bale, Benzema and Cristiano Ronaldo, Ramos, Marcelo and loads of others.