Book value is the shareholders' equity as listed on a company's balance sheet; market value is the market capitalization (# of shares × $/share) of a business.
Market value is calculated by multiplying the number of shares outstanding by the current share price.
Enterprise value is calculated by adding net debt to a company's market value. Net debt is the company's total debts (plus capital leases, certain convertible securities, and non-controlling interests if any) less cash.
Removing cash leaves us with a value that represents the core operating assets of a business.
A market multiple is a multiple based on the current valuation of a company; a purchase multiple is based on the price paid for a company.
Market value is the value of a business after lenders have been paid; EBITDA (before interest) is a metric before lenders have been paid.