The quick answer to this question would be Leonardo Da Vinci. This is the same Leonardo Da Vinci that created drawings of flying machines and autopsied human bodies to learn how muscle groups function. Da Vinci began working on the Mona Lisa sometime between 1503 and 1505 in Florence while he was approximately 52 years old. Da Vinci did not finish the Mona Lisa until many years later, and continued to add layers of paint to the painting over time. Some believe Da Vinci was a perfectionist and therefore continued to work on the Mona Lisa for a very long period of time; others believe Da Vinci had too much going on at once and therefore lost focus.
The woman shown in the painting is generally accepted by most historians as Lisa Gherardini, the wife of Francesco del Giocondo, a silk merchant from Florence. This is how the Italian name "La Gioconda," which roughly translates into English as "The Joyful One," is associated with this particular painting. It's likely that the portrait was commissioned by Francesco to commemorate an event such as the purchase of a new house or the birth of a child, but exactly what is uncertain. Interestingly enough, the family of Francesco never received the painting; Leonardo da Vinci kept possession of the painting and traveled with it, leaving Francesco without his portrait.
The part that people like the best is probably this: On August 21, 1911, the Mona Lisa was stolen from the walls of the Louvre. A man by the name of Vincenzo Peruggia, an Italian handyman who had been employed by the museum, walked out with the Mona Lisa hidden beneath his work smock. No one was able to locate the stolen Mona Lisa for over two years. The reason why she became such a big deal is because of the theft. Newspapers throughout the world ran pictures of her face on the first page of every issue. Vincenzo Peruggia was arrested in December 1913 after attempting to sell the Mona Lisa to an art dealer in Florence. He stated that he wanted to return the Mona Lisa back to Italy. To be honest, there were many Italians who cheered Peruggia.
Today she will be behind a large, thick piece of bullet-proof glass, often with many other individuals holding up their cell phones. Be aware that when you go to see her she is smaller than what most would think; approximately 77 x 53 cm. You will also have very little time to view her closely as you will be moved along by the crowd. There are millions of people who travel to see her each year, and that seems incredible for such a small painting. Some people may feel slightly let down after viewing her, while others may become quite emotional. It appears that people's reactions depend upon their expectations prior to seeing her, and possibly their level of tolerance for being bumped by other people's elbows.
Yes, Leonardo Da Vinci painted her; however, there is much more to this story than simply who created the image. The mysteriousness of her smile, the length of time he used to perfect the image, the theft, the massive amounts of visitors, and so forth, are all adding up to create a legendary status for this painting. Even today, people debate over minor aspects such as if she ever possessed eyebrows, or what she may have been thinking. Perhaps this is exactly why it remains so intriguing. A painting that continues to hold some secrets will always cause people to wonder. Five hundred years later, we continue to gaze upon the painting attempting to decipher the smile.