Connect the feet of the library shelf with the two sides, either in an L-shape or a T-shape, depending on if you have shelves on both sides or on one side. Screw the feet clockwise until snug.
Add two crossbars to the side supports, screwing them in place with the fixing screws. Position the open side of the crossbars facing downward. Place one crossbar at the top and one at the bottom of the shelf supports. This crossbar will add support from side to side, keeping the shelf square.
Slip the adjustable shelving brackets into the holes along the side supports. Install the brackets so they face inward to hold the shelves. Set the brackets at the height you want for the book sizes you plan to display on the shelf.
Attach the shelves to the brackets. Slide the back plates into the groove at the back of the shelf and then screw the shelf in place. Tighten the screws holding the crossbars in place.
Use a level to check how straight the shelving unit is. If necessary, unscrew one or more of the shelf feet just enough to make the whole shelf level.
Attach more units of shelving by attaching more crossbars between an existing shelf side support and a new side support.