This book is quite similar ......

Concept: The adjective "similar" is a fixed preposition collocation — in standard English, "similar" is always followed by "to" (never "with", "of", or "than") to introduce the thing being compared, as in "X is similar to Y".

Application: Here, "this book" is being compared with "the one I read last week", so the blank needs the fixed pairing "similar to", giving: "This book is quite similar to the one I read last week."

Cross-check: Testing each preposition against the collocation rule confirms only one option fits:

• "With" pairs with verbs like "agree with" or "compare with", not with the adjective "similar".

• "Of" typically follows phrases such as "kind of" or "type of", not "similar".

• "Than" is reserved for comparative adjectives ("bigger than", "better than"); "similar" is an equative adjective and never takes "than".

Since only "to" satisfies the "similar + preposition" collocation, the sentence is correctly completed as "This book is quite similar to the one I read last week."