You may find this pdf version of the puzzle more friendly for solving. Please do not put any spoilers in the comments, but feel free to "verify" you have finished the puzzle with me for future recognition by email/private message - upper-left to lower-right diagonal info for each grid should suffice.
Full instructions: 6 common puzzle types are here, following their standard rules, but all of the normal number clues have been replaced with letters. Each digit from 0 to 9 is encoded by exactly two different letters. A letter stands for the same digit in all puzzles in which it appears.
Individual puzzle rules:
Place numbers into the empty cells so that the grid is divided into regions of cells all containing the exact same number. Each region must contain exactly as many cells as the number that it contains. Not all regions are necessarily represented by the given numbers in the grid. Two regions of the same size cannot touch each other, either vertically or horizontally.
Place a number from 1 to 7 into each cell so that no number repeats in any row or column. Also, the clue in the upper-left of each bold cage indicates the value of a mathematical operation (addition, subtraction, or multiplication) applied to all numbers in the cage, starting with the largest number for subtraction.
Place a number from 1 to 6 into each cell so that, in each row and column, every number appears exactly once. Each number in the grid represents the height of a building and the clues on the outside of the grid indicate how many buildings can be "seen" when looking from that direction. Taller buildings block the view of smaller buildings. For example, if a row contained the numbers 15342, then two buildings are seen from the left - 1 and 5 - and three buildings from the right - 2, 4, and 5 - with the other buildings blocked by taller buildings in front of them.
Place a number from 1 to 9 into each cell so that no number repeats in any row, column, or bold region. The numbers in the thermometer shapes must be strictly increasing in each cell from the round bulb to the flat end (ie 12568).
Locate the indicated 10-ship fleet in the grid. Each segment of a ship occupies a single cell. Ships are oriented either horizontally or vertically, and do not touch each other, not even diagonally. Some ship segments, or sea cells without any ship segments, are given in the grid. The numbers on the right and bottom edges of the grid reveal the number of segments in each row/column.
Shade some empty cells black so that the grid is divided into white areas, each containing exactly one number and with the same area as that number. Two white areas may only touch diagonally. All black cells must be connected with each other, but no 2x2 square of cells can be entirely shaded black.