There are many oils available for making soap on the market these days.  Oils with a short shelf life or are prone to rancidity are not recommended as they will also shorten the life of your soap.  Here are some that will give you an idea what you are looking...

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These instructions are intended for use with any basic cold process soap recipe such as the many available on this website, but one is listed to assist you through your first ever soap. Soap making is a time honoured occupation that goes back centuries. Techniques have changed a lot since...