Method for depositing a coating of crystalline metal oxide, nitride or carbide or mixtures thereof, characterized by operating a High Power Impulse Magnetron Sputtering, HIPIMS, discharge on one or more target(s) maintained in the metallic state, in a mixture of argon and a reactive gas, at peak pulse power at least 320 Wcm -2, a pulse length upto 100 μs and a repetition frequency from 100 Hz, wherein - the one or more targets of the same metal composition are of Al, whereby the deposited coating comprises a crystalline phase of alumina, more specifically gamma or alpha alumina, deposited to a thickness of preferably 0.1-30 μm, or, - the one or more targets are of the same metal composition being an AlMe alloy, where Me is one or more of the metals of the group Mg, Zn, Mn, Fe, Co, Ni, Zr, Cd, Cu, Cr and Sn and the gas mixture in the vacuum chamber is a mixture of Ar and oxygen gas (O 2), whereby the deposited coating comprises a two phase oxide, or a mixed oxide of the type (Al 1-x Me x) 2 O 3 or spinel (Me) x Al 2 O 3+x (0<x≤1), or, - two or more targets, having metal compositions differing from each other, and a gas mixture of Ar and oxygen gas(O 2), is used, whereby a multilayer or mixed oxide of the type (Al 1-x Me x) 2 O 3 or spinel (Me) x Al 2 O 3+x (0<x≤1), or a two phase oxide is deposited, where Me is one or more of the metals of the group Mg, Zn, Mn, Fe, Co, Ni, Zr, Cd, Cu, Cr and Sn or, - cutting tools of suitable types, provided as substrates, are coated, in a vacuum chamber, with a metal oxide, nitride, carbide or mixtures thereof by using a reactive gas mixture comprising oxygen, nitrogen and/or carbon containing gases, the one or more targets are of the same metal composition being an AlMe alloy, where Me is one or more of the metals of the group Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W, the deposition is initiated in pure Ar sputtering gas or start in conjunction with, or after, introducing the reactive gas through the second valve or mass flow controller, or, - two or more targets have a metal composition differing from each other, whereby mixed or multilayered AlMe coatings of oxide, nitride, carbide or mixtures thereof are obtained, where Me is one or more of the metals of the group Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W. - the one or more targets of the same metal composition are of Al, whereby the deposited coating comprises a crystalline phase of alumina, more specifically gamma or alpha alumina, deposited to a thickness of preferably 0.1-30 μm, or, - the one or more targets are of the same metal composition being an AlMe alloy, where Me is one or more of the metals of the group Mg, Zn, Mn, Fe, Co, Ni, Zr, Cd, Cu, Cr and Sn and the gas mixture in the vacuum chamber is a mixture of Ar and oxygen gas (O 2), whereby the deposited coating comprises a two phase oxide, or a mixed oxide of the type (Al 1-x Me x) 2 O 3 or spinel (Me) x Al 2 O 3+x (0<x≤1), or, - two or more targets, having metal compositions differing from each other, and a gas mixture of Ar and oxygen gas(O 2), is used, whereby a multilayer or mixed oxide of the type (Al 1-x Me x) 2 O 3 or spinel (Me) x Al 2 O 3+x (0<x≤1), or a two phase oxide is deposited, where Me is one or more of the metals of the group Mg, Zn, Mn, Fe, Co, Ni, Zr, Cd, Cu, Cr and Sn or, - cutting tools of suitable types, provided as substrates, are coated, in a vacuum chamber, with a metal oxide, nitride, carbide or mixtures thereof by using a reactive gas mixture comprising oxygen, nitrogen and/or carbon containing gases, the one or more targets are of the same metal composition being an AlMe alloy, where Me is one or more of the metals of the group Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W, the deposition is initiated in pure Ar sputtering gas or start in conjunction with, or after, introducing the reactive gas through the second valve or mass flow controller, or, - two or more targets have a metal composition differing from each other, whereby mixed or multilayered AlMe coatings of oxide, nitride, carbide or mixtures thereof are obtained, where Me is one or more of the metals of the group Ti, V, Cr, Zr, Nb, Mo, Hf, Ta, and W.