A sub-nanometer resolution Scanning Nonlinear Dielectric Microscope (SNDM) was developed for observing ferroelectric polarization. We also demonstrate that the resolution of SNDM is higher than that of a conventional piezo-response imaging. Secondly, we report new SNDM technique detecting higher nonlinear dielectric constants $varepsilon$$\_$3333/ and $varepsilon$$\_$33333/. Higher order nonlinear dielectric imaging provides higher lateral and depth resolution. Finally, the formation of artificial small inverted domain is reported to demonstrate that SNDM system is very useful as a nano-domain engineering tool. The nano-size domain dots were successfully formed in LiTaO$_3$ single crystal. This means that we can obtain a very high density ferroelectric data storage with the density above 1T-bits/inch$^2$.