A little background, however, could be helpful.
No one knows when the Tangram was invented. It was certainly invented in China, however, and was popular there for many years before foreigners were introduced to its delights. It eventually made its way to the west when, in 1815, Captain Edward Milner Donnaldson (1778-1853) docked his ship, Trader, in Canton. While there, he was given a pair of Sang-Hsia-koi's Tangram books. He brought those books with him to Philadelphia in February 1816 and they became the basis for the first book of Tangrams to be published in the USA. [As an aside, you can learn a little about Captain Donnaldson and his family by clicking here and searching for his name.]
The Tangram craze really began when, in 1903, the great American puzzler Sam Loyd published The Eighth Book Of Tan. In it, he included about 700 shapes to copy/reproduce. He also included a fascinating, but totally ficticious, history of Tangrams in which he claimed they were invented 4,000 years earlier by a god called Tan. The craze rapidly spead to other countries.
So, what is the Tangram and how do you 'play' it?
It is simply a game in which you rearrange seven shapes to match some given illustration. The seven shapes are cut from a square such as the one above. You can purchase a Tangram set (they are made out of a huge variety of materials), or you can make your own, or you could simply click on the image above and print out a pattern and cut it into seven pieces. You then try to arrange them to make pictures like the one at the right (you may need to flip the parallelogram for some patterns). Usually, however, the outlines of the shapes are not provided, and that is what creates the challenge!
I mentioned that there are many resources on the Internet. To find them, you could simply Google 'Tangrams', or you could go straight to one site that I found, Tangram Channel, that seems to be very well set up with lots of information and challenges.