Minimum tools:
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Steel Ruler/straight edge: Make/cut straight lines
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Marking tool: scratch awl or pen
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Cutting tool: Knife for cutting leather. Some use specialty leather knives. Others use box cutters/ Xacto's.
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Stitching Divider/ Wing Divider: To make the guide to follow when punching your stitch holes.
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Pricking Irons/Chisels: Different TPI depending on how thick your leather is. There are also different styles: straight, diamond etc. It'll affect the over all look of the piece.
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Mallet: Plastic or wood. Steel is too hard for the pricking irons and rubber is too soft.
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Leather awl: For punching through leather after using pricking iron.
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Thread: Thickness will depend on the TPI of your pricking irons. This will affect the look of the stitching.
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Needles: Saddle stitching needles come in different sizes depending on the thickness of your thread.
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Glue: There are some specifically made for leather work. Some people just use Barge cement.
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Small Clamps: For keeping leather together as the glue dries.
Extra tools:
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Punches with specific shapes. Circles, semicircles etc
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Edge Beveler: To bevel leather edges before burnishing
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Leather burnisher: To finishs the edges.
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Edge finish: Gum, Beeswax, Tokonole, edge paint
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Lighter: To finish a stitch
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Oils/ conditioners: To maintain the leather
I probably missed some things.
Edit: For the snaps you need a snap setter.