Catalyst including active particles, method of preparing the catalyst, fuel cell including the catalyst, electrode including the active particles for lithium air battery, and lithium air battery including the electrode

A catalyst including active particles that have a core including a first metal oxide, and a shell including an alloy of a second metal with a reduction product of the first metal oxide; a method of preparing the catalyst; a fuel cell including the catalyst; an electrode for lithium air battery that includes the active particles; and a lithium air battery including the electrode.