This series introduces Logo programming for beginners. These 12 challenges are written for you to work through at your own pace.
You don't need to know anything about programming at the start: you will learn enough at the first stage to write your own programs, and you may surprise yourself by how much you can achieve right away.
Windows users can download a free copy of FMSlogo.
A good free version for Mac users is ACSlogo.
There's a version you can run directly in your browser at http://calormen.com/logo/.
First Forward into Logo 1: Square Five
First Forward Into Logo 2: Polygons
First Forward Into Logo 3: Repeat REPEAT
First Forward into Logo 4: Circles
First Forward into Logo 6: Variables and Procedures
First Forward into Logo 7: Angles of Polygons
First Forward into Logo 8: More about Variables
First Forward into Logo 10: Count Up - Count Down
First Forward into Logo 11: Sequences
First Forward into Logo 12: Puzzling Sums
Unfortunately logo is really the name of a family of languages, rather than one single standard language. You can't expect programs written for one logo to run unchanged in another implementation.
Once you have picked up a taste for programming, try moving on to other more useful languages. We'd recommend Processing (java) or Nodebox (python) for graphics, or the excellent Eloquent Javascript text as an introduction to web programming.
For general purpose mathematical programming, try python or ruby. Both these languages can handle integer arithmetic without introducing rounding errors, and there are plenty of free web resources to get you started.