The Statue of Liberty was originally known as Liberty Enlightening the World. It was given to the United States by France to celebrate their alliance during the Revolutionary War. A sculptor by the name of Frédéric Auguste Bartholdi designed the statue, and Gustave Eiffel (the man who designed the Eiffel Tower) was responsible for the iron framework underneath the copper plating.
The statue was built in Paris and then shipped to the U.S. in 1885. Various parts of the statue were on display throughout Paris as they were completed. Miss Liberty's head was exhibited in the gardens at the Tracadéro, and her torch was on display as well, as you can observe in the images on this page.
Construction began in 1875 and was not completed until 1884. Crews worked round the clock, seven days a week, for nine years to finish the Statue of Liberty. When it was complete in 1885, the statue was disassembled into 350 pieces, shipped to New York City, and reassembled. It took 4 months just to put the Statue of Liberty together again!
The Statue of Liberty was officially dedicated and unveiled on October 28, 1886.
A collection was taken up in France to fund the statue, raising 2,250,000 francs ($250,000 U.S. dollars). It doesn't look like much, but $250,000 in the 19th century would be the same as millions of dollars today. Both the U.S. and France participated in fundraising activities, and it took a very long time to raise enough money to finish construction.