Published first in 1914, by Maria Montessori.
I think the aim of this book was to help the large number of people interested in her method, to understand what it is all about. There is a bit of theory, but mostly the book focusses on the materials and how they work and how they relate to each other.
The materials are incredably intricate for their simplicity. The sensory materials are in decimals, 1 to 10 cm. They teach so much, it's hard to describe. Sensory wise they teach volume and order, both are important pre-math skills. But they also teach precision and concentration. Counting and numbers. The knobbed cylinders teach pencil grip. The rest teach gross (moving the large cubes) and fine (moving the 1cm3 cube) motor skills. It teaches how to carry things and be careful and respectful with materials. It teaches work ethic.
The materials come in order: knobbed cylinders, pink tower, brown stairs, red rods, red and blue rods and finally the knobless cylinders.
She also discusses other materials for training the senses, such as baric tablets, sandpaper tablets, sound cylinders, bells, metal insets, beads, colour tablets and much more. But also practical life skills, and the necessary materials for them. She explains their purpose and what the children are learning from them.
It's a great little book. Easy to read and very practical. It goes through most materials, explaining why, how and which way. It's all very precise. Not all materials are mentioned and I wouldn't be surprised if some got developped after this book was written.
There are many books aimed at parents, that probably use easier language and clearer instructions. This book is perhaps better for when you already got a bit of an idea and want to get into the material a bit deeper