Before matador enters the ring, two picadors on horse use lance (pica) to injure the bull, and cut open the bull's shoulder. This is to irritate the bull and make its fight against the matador more exciting. And it opens up a small cut between the bull's shoulder blades for matador to enter the sword during the final stroke for the kill. Also it makes the bull bleed and weaken gradually towards the end. Picadors are least respected in the ring because they sit high up on horseback without showing courage.
Although controversial, bullfights are Mexicans' favorite passtime. One may argue it's too cruel and not a real sport, but in Mexicans' eyes it's sport, entertainment, dance, and an art form full of rituals and traditions. It's not my job to pass judgment here.
Corridas de toros means charging of the bulls in English. Throughout the fight, both the matador and the bull are expected to show tremendous courage. The matador can get hurt or killed in any second, and the bull eventually gets killed. But in rare cases, if the bull shows exceptional courage it may be spared of its life, then sent to stud for the rest of its life. Not a bad deal.
Flamenco is the traditional Spanish dance adopted by the Mexicans. Similar to the bullfights, it's now an intergral part of Mexican culture. Besides the costume, the dance requires lots of clapping and foot work such as kicking and stumping. The dances shown in photo were performed outside the arena before the bullfights.
In the begining of a bullfight, matador's assistants run around the ring (no cape, no sword) to tease the bull. The bull gets annoyed and charges towards the assistants at full speed until the assistants find shelter. This is to show off the strength, speed, and vigor of the bull to the audience.
In the end of a bullfight, the matador kills the bull and the bull is dragged out of the ring. This is how Hemingway got the name for his book, Death in the Afternoon. If the matador has been very brave, the bull's ears (1 or 2, depending on how brave) will be cut off and presented to the matador. It's determined by the audience.
Outside the bullfight arena a group of animal right activists gather to protest. Fortunately everything was peaceful; no conflict between the activists and the audience.