Faith in Nature (just as an illustration) is a cold processed soap with the folowing ingredients in their lavendar bar...
Sodium Palmate (palm oil)
Sodium Cocoate and/or Sodium Palm Kernelate (coconut oil or palm kernal oil)
Aqua (water)
Glycerin (a moisturising by product of the chemical reaction, some makers add extra to make it extra moisturising; it essentially creates a misture barrier on your skin to trap the moisture in, plus attracts moisture from the air)
Lavandula Angustifolia Oil (lavender oil)
Lavandula Hybrida Oil (diff type of lav. oil)
Sodium Chloride (lye - it's this that reacts with the fats etc to make soap)
Sodium Citrate (citric acid that helps prevent the bar creating soap scum)
Linalool (a chemical found in many flowers and spices and used as a foundation for the scent)
Limonene (citrus based extract that helps with cleaning and smells nice)
Geraniol (another scent chemical, found in things like rose oil)