An extraction and separation method for extracting and separating a specific component from a raw material fluid, comprising: an extraction and separation step of extracting and separating the specific component from the raw material fluid, using an extraction device including a plurality of stages of extraction sections (4, 5, 6, 7, 8) sequentially connected to one another, wherein the extraction and separation step includes: an extraction step of extracting the specific component from the raw material fluid to an extracting agent while the raw material fluid and the extracting agent having a specific gravity difference relative to the raw material fluid are allowed to flow in the extraction section (4, 5, 6, 7, 8) at each stage while being in contact with each other; and a final separation step of separating the fluid discharged from the extraction section (4, 5, 6, 7, 8) at a final stage into the raw material fluid from which the specific component has been extracted and the extracting agent that has extracted the specific component, characterized by a feeding step of feeding at least a part of the fluid discharged from the extraction sections (4, 5, 6, 7, 8) into the subsequent extraction sections (4, 5, 6, 7, 8) while the raw material fluid and the extracting agent are mixed with each other, wherein, in the extraction and separation step, the extraction device in which the extraction section (4, 5, 6, 7, 8) at each stage includes an extraction flow passage through which the fluid that has been fed into the identical extraction section (4, 5, 6, 7, 8) is allowed to flow, and each extraction section (4, 5, 6, 7) other than at least the extraction section at the final stage includes a discharge portion (27, 43, 49, 55) connected to an outlet port of the extraction flow passage is used, and the feeding step includes an each stage separation step of separating, in each extraction section (4, 5, 6, 7) other than the extraction section at the final stage, the fluid discharged from the extraction flow passage to the discharge portion (27, 43, 49, 55) into a first fluid and a second fluid due to a specific gravity difference and performing separation such that the first fluid contains the raw material fluid and the extracting agent, and a separated fluid feeding step of feeding the first fluid separated in the discharge portion (27, 43, 49, 55) in the each stage separation step into the extraction flow passage of the subsequent extraction sections (4, 5, 6, 7, 8). an extraction and separation step of extracting and separating the specific component from the raw material fluid, using an extraction device including a plurality of stages of extraction sections (4, 5, 6, 7, 8) sequentially connected to one another, wherein the extraction and separation step includes: an extraction step of extracting the specific component from the raw material fluid to an extracting agent while the raw material fluid and the extracting agent having a specific gravity difference relative to the raw material fluid are allowed to flow in the extraction section (4, 5, 6, 7, 8) at each stage while being in contact with each other; and a final separation step of separating the fluid discharged from the extraction section (4, 5, 6, 7, 8) at a final stage into the raw material fluid from which the specific component has been extracted and the extracting agent that has extracted the specific component, characterized by an extraction step of extracting the specific component from the raw material fluid to an extracting agent while the raw material fluid and the extracting agent having a specific gravity difference relative to the raw material fluid are allowed to flow in the extraction section (4, 5, 6, 7, 8) at each stage while being in contact with each other; and a final separation step of separating the fluid discharged from the extraction section (4, 5, 6, 7, 8) at a final stage into the raw material fluid from which the specific component has been extracted and the extracting agent that has extracted the specific component, characterized by a feeding step of feeding at least a part of the fluid discharged from the extraction sections (4, 5, 6, 7, 8) into the subsequent extraction sections (4, 5, 6, 7, 8) while the raw material fluid and the extracting agent are mixed with each other, wherein, in the extraction and separation step, the extraction device in which the extraction section (4, 5, 6, 7, 8) at each stage includes an extraction flow passage through which the fluid that has been fed into the identical extraction section (4, 5, 6, 7, 8) is allowed to flow, and each extraction section (4, 5, 6, 7) other than at least the extraction section at the final stage includes a discharge portion (27, 43, 49, 55) connected to an outlet port of the extraction flow passage is used, and the feeding step includes an each stage separation step of separating, in each extraction section (4, 5, 6, 7) other than the extraction section at the final stage, the fluid discharged from the extraction flow passage to the discharge portion (27, 43, 49, 55) into a first fluid and a second fluid due to a specific gravity difference and performing separation such that the first fluid contains the raw material fluid and the extracting agent, and a separated fluid feeding step of feeding the first fluid separated in the discharge portion (27, 43, 49, 55) in the each stage separation step into the extraction flow passage of the subsequent extraction sections (4, 5, 6, 7, 8).