The aggregation structure of fatty acid monolayers on the water surface have been classified with respect to thermal (T-sp, T-alpha c, T-m) and chemical (the degree of ionic dissociation of hydrophilic group) factors. In the cast of amphiphiles with a non-ionic hydrophilic group, at T-sp below T-m, the monolayer is in a crystalline phase which is designated "the crystalline monolayer". The crystalline monolayer is further classified into "the fusing-oriented crystalline monolayer" and "the randomly assembled crystalline monolayer" at T-sp below and above T-alpha c, respectively. At T-sp above T-m, the monolayer is in an amorphous phase which is designated "the amorphous monolayer". in the case of amphiphiles with an ionic hydrophilic group, at T-sp below T-m, amphiphile molecules form "the compressing crystallized monolayer", and T-sp above T-m, the monolayer is not crystallized by compression. Molecular-resolution images of molecules in the monolayers were successfully observed with an atomic force microscope (AFM) for the first time. A high mechanical stability of the monolayer is inevitably required for the non-destructive AFM observation of the fatty acid monolayer. For the preparation of the mechanically stable monolayer, the continuous compression method up to a low surface pressure and the multi-step creep method were used. Further, the Langmuir-Blodgett (LB) films with a homogeneous surface morphology could be constructed by the mechanically stable monolayers, and the morphological homogeneity was necessary for the construction of low-propagation loss LB film optical waveguides.