IAS 32 classifies financial instruments into four main categories:

1. Financial assets measured at amortized cost: These are financial assets that are held for the purpose of collecting contractual cash flows and have fixed or determinable payments. The criteria for classification as financial assets measured at amortized cost are that the asset is not held for trading and there is no intention to sell it in the near term.
2. Financial assets held for trading: These are financial assets that are acquired for the purpose of selling or repurchasing them in the near term. The criteria for classification as financial assets held for trading are that the asset is held for the purpose of short-term profit-taking or it is a part of a portfolio of identified financial instruments that are managed together for short-term profit-taking.
3. Financial assets available for sale: These are financial assets that are not held for trading, are not classified as financial assets measured at amortized cost, and are not held to maturity. The criteria for classification as financial assets available for sale are that the asset is not held for the purpose of collecting contractual cash flows or short-term profit-taking.
4. Financial liabilities measured at amortized cost: These are financial liabilities that are held for the purpose of paying contractual cash flows and have fixed or determinable payments. The criteria for classification as financial liabilities measured at amortized cost are that the liability is not held for trading and there is no intention to repay it in the near term.

The classification of financial instruments under IAS 32 is important because it affects how they are subsequently measured, presented, and disclosed in the financial statements.