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Step-by-step build — 3 steps. Also available as a print sheet.
Draw your end curve on one side — staying inside the top and bottom 4", because that's where the outer shelves land — cut it with the jigsaw, sand it fair, and trace it onto the second side. Cut and sand that one to the line.
While both sides are clamped together, mark every shelf position across both at once: top and bottom shelves 4" in from the ends, the middle two spaced 10" apart. Shelves are 3/4" thick — mark both edges of each so nothing lands a half-thickness off.
Glue and fasten the four shelves between the sides on your layout marks — 2" brads or screws, three per joint. Square the assembly by matching diagonals before the glue sets; a shelf unit assembles as a parallelogram with astonishing ease.
Add the two 1x2 cleats flush to the back: one tight under the top shelf, one on top of the bottom shelf. Glue and brads.
Fill the brad holes, sand, and paint — a painted build forgives every filled hole.
Find the studs, level the shelf, and drive the 3" screws through both cleats into framing. The cleats exist precisely so this step is boring: real screws, real wood, real studs, and a shelf that holds actual books instead of decorative ones.