On page 104, Volume 3(Economics), the relative strength approch to predicting currency values says that if a country has high interest rates, the currency will appreciate. But according to Interest rate parity, the currency should depreciate. Which is correct? Thank you.

The country with the higher real rate will appreciate. I believe Interest Rate Parity assumes that real rates are equal and nominal rates are different.

If the real interest rates increase only then the currency increases.

Yes assumption of interest rate parity is that real rates are the same accross countries. This assumes free capital flows and integration. If markets are not integrated, real rates of return differences may be available. Therefore if markets are liberated, the currency value of the market with higher real rates of return will appreciate. In integrated markets we assume that capital flows will balance out real rates of return, flowing to higher rates if available. In this case, uncovered interest rate parity says that any differential between interest rates is due to inflation and the currency of the country with the higher interest rate will depreciate.