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Blocks are required to construct certain buildings such as furnaces and wells. They can also be used in place of raw stone or other materials to construct nearly any other type of building.
Bridges, roads, and aqueducts made out of blocks will be "smooth" instead of "rough" (when made out of raw stone). The only known advantage of smooth bridges and roads is that they can be built more quickly (twice as fast as rough) and that they have a higher monetary value (a fortress's road must be of a certain value to attract a king). Blocks have a base value of 5☼, which is multiplied by their material value and the design and construction quality of the construction they are used in. Raw stones have a base value of 0☼, so no matter how well a raw stone construction is built, it will never have a monetary value, only providing a small amount of architecture value.
Blocks are usually made from stone (in a mason's workshop) due to its abundance. They can also be fashioned out of any type of glass at a glass furnace, or any metal at a metalsmith's forge. Blocks can be stored in bins, but raw stone cannot. Blocks are a little bit lighter than raw stone (250Γ instead of 300Γ), and so dwarves will be slightly less encumbered when carrying them.
Green glass blocks have two advantages. They have a material value of 2x, the same as light stone or non-obsidian dark stone. In addition, the only material they require is sand, which must be gathered before it can be used, but which is available in unlimited amounts.
Clear glass blocks have a material value of 5x, considerably more than any type of stone, but in addition to sand, they require pearlash. Pearlash takes time and effort to produce, but it is made from wood, a renewable resource.
Crystal glass blocks have a material value of 10x, the same as iron, but they also require rough rock crystals which are very limited in supply.
Metal blocks are not made from renewable resources (unless you count goblinite), but they have a few advantages. Blocks of expensive metals can be used to build extremely valuable roads. They can also be used in an exploit to bridge over the magma flow. Bridges over the magma flow must be steel or adamantine. However, the game only looks at the material highest in the material list to determine what a bridge is made of. Metal bars are the last objects in the material list, so this is generally exploited by selecting one bar of steel and building the rest of the bridge out of a low-value metal, such as brass. Blocks are sorted second in the material list, after raw stone but before wood logs and metal bars, so it is possible to bridge the magma flow by selecting one block of steel and building the rest of the bridge from blocks of stone or even wood logs further down the list.
Other than the above exploit, metal blocks have no advantages over metal bars in building bridges or aqueducts, and they have an additional step in the production process, so it is more efficient to just build with bars instead. They can be used to construct most buildings, while bars cannot (with the sole exception of magma forges and the magma furnaces). However, there is no advantage to making a building out of metal blocks instead of stone or glass. The most impressive trait of metal blocks is that they weigh more than the bar they are made from (250Γ for the block, 200Γ for the bar); they are therefore a useful way to prove the falsehood of the law of conservation of mass.
When dwarves enter strange moods and ask for a "proper surface" or "square blocks", they want stone blocks. Sometimes they may want light or dark stone blocks instead of gray blocks; it is good to make a few of each color ahead of time. Note that completed artifacts that use blocks do not have the blocks listed as an ingredient in their description. Apparently the dwarves use the blocks as working surfaces and then destroy them afterward.
Buildings which require blocks in their construction (metalsmith's forge, alchemist's laboratory, ashery, well, and all non-magma furnaces) can only be built using gray stone blocks - blocks made from light stone, dark stone, glass, or metal cannot be used for these.
Blocks made of flux (i.e. limestone) cannot be used for making pig iron or steel.