Sylvius Leopold Weiss (1687 - 1750) was one of the greatest composers who wrote for the lute and one of the best known lutenist of his day. This Gigue is apparently from the Dresden manuscript but I could not discover which sonata it belongs to. Later on in his life, Weiss became friends with Wilhelm Friedemann Bach, the eldest son and second child of Johan Sebastian Bach. It is said that Weiss and Bach competed in improvising fugues and fantasies. For more information http://www.slweiss.com.
I could not find any guitar performances of this piece on YT. Which surprises me because, although not easy, this piece is a lot of fun to play. My rendition is far from perfect. There are a couple of mistakes and the tempo should be a bit faster. I recommend a speed of 3 quavers = 100. I hope you enjoy it, mistakes and all.
Thanks for listening.