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We construct infinitely many new 1-parameter families of simply connectedcomplete noncompact G_2-manifolds with controlled geometry at infinity. Thegeneric member of each family has so-called asymptotically locally conical(ALC) geometry. However, the nature of the asymptotic geometry changes at twospecial parameter values: at one special value we obtain a unique member ofeach family with asymptotically conical (AC) geometry; on approach to the otherspecial parameter value the family of metrics collapses to an AC Calabi-Yau3-fold. Our infinitely many new diffeomorphism types of AC G_2-manifolds areparticularly noteworthy: previously the three examples constructed by Bryantand Salamon in 1989 furnished the only known simply connected AC G_2-manifolds.  We also construct a closely related conically singular G_2 holonomy space:away from a single isolated conical singularity, where the geometry becomesasymptotic to the G_2-cone over the standard nearly K\"ahler structure on theproduct of a pair of 3-spheres, the metric is smooth and it has ALC geometry atinfinity. We argue that this conically singular ALC G_2-space is the naturalG_2 analogue of the Taub-NUT metric in 4-dimensional hyperKaehler geometry andthat our new AC G_2-metrics are all analogues of the Eguchi-Hanson metric, thesimplest ALE hyperK\"ahler manifold. Like the Taub-NUT and Eguchi-Hansonmetrics, all our examples are cohomogeneity one, i.e. they admit an isometricLie group action whose generic orbit has codimension one.

Infinitely many new families of complete cohomogeneity one G_2-manifolds: G_2 analogues of the Taub-NUT and Eguchi-Hanson spaces