a.k.a. Mix Box
Brevettato (patented), Italy, circa 1980's
(cardboard box and plastic puzzle, 5 inches by 7/17 inches thick)

A 4 by 4 grid can be manipulated by sliding the rows and columns by one square. The top row can only move one square to the right, the second row one square to the left, the third row one square to the right, and the fourth row one square to the left. Similarly, the left column can only move one square up, the second column one square down, the third column one square up, and the fourth column square down. Mix it up and then solve to one of the patterns that are shown in the directions that were sold with the puzzle:

This puzzle is similar to Rubik's XV and Tsukuda's Square. Jaap's Page presents a solution that first observes that a local permutation of three squares can be achieved by the sequences of four moves consisting of sliding a row, a column, the row back, and the column back, and then solves by first placing the four corners and then repeatedly using this transformation to solve the remaining squares.

Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/uriblock.htm