A family of methods is introduced for creating, manipulating and observing nuclear singlet spin order. The basic element is conversion between longitudinal magnetisation and singlet spin order, M2S and S2M. It is based on near-resonance radio-frequency pulses of adiabatically varying amplitude that guide the spins through regions of avoided level-crossings of the system. After discussing the theoretical concepts, we illustrate the practical application of such Adiabatic Passage Spin Order Conversion (APSOC) by analysing the relaxation decay of singlet order independent of the coupling strength of the spin pair. By combining several such pulse sequences and varying their carrier frequency, a filter is designed for Singlet Order Selection (SOS) and suppression of all other spectral components. It enables background-free detection of selected spin pairs. To ease the constraint of slow amplitude variation while staying within the limits of adiabaticity the pulse amplitude profile is shaped so that only near level-crossings speed is reduced, but increased elsewhere; optimum control methods are used to find the ideal pulse shape. In this way adverse relaxation effects during pulses are minimised. Conversion factors close to the theoretical maximum are thus achievable. With such a toolbox not only highly efficient conversion is possible, but also other manipulations of spin order, e.g. polarisation transfer between different spin species or anti-phase to in-phase transformation of spectral components.