In order to be able to investigate the chemical history of the entire MilkyWay, it is imperative to also study the dust-obscured regions, where most of the mass lies, in detail. The Galactic Center is an example of such a region of interest to study. Due to the intervening dust along the line-of-sight, near-infrared spectroscopic investigations are necessary. The aim is to demonstrate that M giants observed at high spectral resolution in the H and K bands (1.5-2.4um) can yield useful abundance-ratio trends versus metallicity for 21 elements. These elements can therefore be studied also for heavily dust-obscured regions of the Galaxy, such as the Galactic Center. The abundance-ratio trends will be important for the further investigation of the Galactic chemical evolution in these regions. We have observed near-infrared spectra of 50 M giants in the solar neighbourhood at high signal-to-noise and at a high spectral resolution with the IGRINS spectrometer on the GEMINI South telescope. The full H and K bands are recorded simultaneously at R=45000. We adopted the fundamental stellar parameters for these stars from Nandakumar et al. (2023A&A...675A..23N, Cat. J/A+A/675/A23), with Teff ranging from 3400 to 3800K. With a manual spectral synthesis method, we have derived stellar abundances for 21 atomic elements, namely F, Mg, Si, S, Ca, Na, Al, K, Sc, Ti, V, Cr, Mn, Co, Ni, Cu, Zn, Y, Ce, Nd, and Yb.We have systematically studied useful spectral lines of all these elements in the H and K bands. We demonstrate what elements can be analysed from H- and K-band high-resolution spectra, and we show which spectral lines can be used for an abundance analysis, showing them line by line.We discuss the 21 abundance-ratio trends and compared them with those determined from APOGEE and from the optical GILD sample. Especially, the trends of the heavy elements Cu, Zn, Y, Ce, Nd, and Yb are possible to retrieve from high-resolution H- and K-band spectra. This opens up these nucleosynthetic channels, including both the s- and the r-process, in dust-obscured populations. The [Mn/Fe] versus [Fe/H] trend is shown to be more or less flat at low metallicities, implying that existing NLTE correction are relevant. With high-resolution, near-infrared spectra it is possible to determine reliable abundance-ratio trends versus metallicity for 21 elements, including elements formed in several different nucleosynthetic channels. The important neutron-capture elements, both s- and r-dominated elements, are doable. This opens up the possibility to study the chemical evolution in detail also in dustobscured region of the Milky Way, such as the Galactic Center. M giants are useful bright probes for these regions and for future studies of extra-galactic stellar populations. A careful analysis of high quality spectra is needed to retrieve all these elements, often from weak and blended lines. A spectral resolution of R~40000 is a further quality which helps in deriving precise abundances for this range of elements. In comparison to APOGEE, we can readily obtain the abundances for Cu, Ce, Nd and Yb from the H-band, which demonstrates an advantage of analysing high-resolution spectra