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A complete derivation of a new two-variable integrodifferential equation valid for threeand many-boson systems is given here for the first time, and it is shown to be exact if all correlations higher than those of two-body type can be neglected. Its equivalence to the Faddeev equation for three bodies and its applicability to many-body systems are discussed in detail. Three-body forces are included. It is shown that the threeand four-body binding energies obtained by means of this equation are in good agreement with those obtained from the most sophisticated variational, Faddeev, and Faddeev-Yakubovsky calculations. This indicates that our new two-variable integrodifferential equation should also be useful for larger systems, in particular since unlike other methods it does not suffer from the disadvantage of rapidly increasing complexity with A. We also show that a simple adiabatic method for the solution of this equation {and hence also for the Faddeev equation) is quite sufficient, due to the closeness of the upper and lower bounds obtained in this way. Finally we apply the adiabatic method to nuclear three-body scattering and even include the effect of breakup for spin-dependent forces. It is found that asymptotic behavior is reached for a value of the hyperradius of the order of 3S fm.where

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