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The Eguchi-Hanson, Taub-NUT and Atiyah-Hitchin metrics are the only completenon-singular SO(3)-invariant hyper-Kahler metrics in four dimensions. Thepresence of a rotational SO(2) isometry allows for their unified treatmentbased on solutions of the 3-dim continual Toda equation. We determine the Todapotential in each case and examine the free field realization of thecorresponding solutions, using infinite power series expansions. TheAtiyah-Hitchin metric exhibits some unusual features attributed to topologicalproperties of the group of area preserving diffeomorphisms. The construction ofa descending series of SO(2)-invariant 4-dim regular hyper-Kahler metricsremains an interesting question.Comment: A few typos have been corrected; final versio

Toda Fields of SO(3) Hyper-Kahler Metrics and Free Field Realizations