The basicity of amines increases with the number of electron-donating groups attached to nitrogen. Alkyl groups are electron-donating, which increases the electron density on nitrogen, making it more basic. Therefore, the increasing order of basicity is: \[ \text{NH}_3<\text{CH}_3\text{NH}_2<(\text{CH}_3)_2\text{NH}<(\text{CH}_3)_3\text{N} \]