An analysis of an object dyed with fluorescent coloring agents carried out with the aid of a fluorescent microscope which is modified for improved resolving power and called a nanoscope. The method is carried out with a microscope having an optical system for visualizing and projecting a sample image to a video camera which records and digitizes images of individual fluorescence molecules and nanoparticles at a low noise, a computer for recording and processing images, a sample holder arranged in front of an object lens, a fluorescent radiation exciting source and a set of replaceable suppression filters for separating the sample fluorescent light. Separately fluorescing visible molecules and nanoparticles are periodically formed in different object parts, the laser produces the oscillation thereof which is sufficient for recording the non-overlapping images of the molecules and nanoparticles and for decoloring already recorded fluorescent molecules, wherein tens of thousands of pictures of recorded individual molecule and nanoparticle images, in the form of stains having a diameter on the order of a fluorescent light wavelength multiplied by a microscope amplification, are processed by a computer for searching the coordinates of the stain centers and building the object image according to millions of calculated stain center co-ordinates corresponding to the co-ordinates of the individual fluorescent molecules and nanoparticles. With this invention it is possible to obtain a two-dimensional and a three-dimensional image with a resolving power better than 20 nm and to record a color image by dyeing proteins, nucleic acids and lipids with different coloring agents.