Intaglio is comprised of etching, aquatint, drypoint and engraving.  It is rumored to have begun in the middle ages with smiths engraving armor, rubbing ink into the designs and printing them to make a record of their work. It later became the standard for mass-produced illustrations in books and replications of famous artworks, as well as a fine art medium unto itself. To create an intaglio print, a plate of either copper or zinc is coated with a resist (traditionally asphaltum and beeswax) which the artist scratches through to make lines. The plate is then dipped in nitric acid which bites into the areas that have been scratched. The lines can also be carved by hand (called drypoint or engraving depending on the tool used). Aquatint is a method for creating areas of value which involves dusting the plate and cooking it, but I'll spare you the magic details.

To print the plate, ink is wiped across it and pushed into the etched areas. The excess is wiped off of the surface. The plate is run through a high-pressure press with softened (wet) paper which is pushed into the etched parts, picking up the ink. This process is repeated for every print pulled. Most prints are hand printed in small editions (hence the number at the bottom 1/10), and are all fine art originals (not the same as machine made reproductions). Intaglio prints are recognizable by their distinct plate mark, where the plate has embossed the paper.  (Rembrandt and Durer revolutionized this medium; and Paula Rego and Kiki Smith make amazing intaglio prints).

Relief printmaking, also known as woodcut (or wood engraving/carving) and linocut (or linoleum block carving) is basically like a stamp.  The areas that are to remain white in the image are carved away, leaving areas to be inked with a roller (brayer).  Carving a potato or eraser stamp is relief printing.  Wood engraving was also a very popular printing method for mass-produced book illustrations and reproductions of famous artworks.  Kathe Kollwitz is one of my favorite artists who rocked this medium.

Serigraphy is the fancy name for screen-printing or silkscreen.  It is like a stencil (it is a stencil).  The screen's purpose is help distribute ink evenly instead of just having the area be open.  A squeegee is pulled across the screen pushing ink onto the paper below.  The artist can use a variety of materials (vinyl, varnish) as stop-outs to keep areas of the screen from letting ink through.  Serigraphy was popular with the Pop Artists (Roy and Andy) and is a DIY revolution right now.

Lithography is a planographic process functioning on the principle that water and oil resist one another.  The image is drawn on a special type of Bavarian limestone with an oil-based medium.  Then a magical etching/adsorption process happens and the drawing becomes chemically part of the surface.  The stone is kept wet while printing so that the oil-based ink will not stick to the non-image areas, but will stick to where you drew. Yep, that's how it works: Bavarian limestone and adsorption.  Litho took over as the preferred illustration production method in the 19th century (think Mucha and Le Chat Noir posters).