Samuel Hahnemann, the founder of homœopathy, was a highly educated man who spoke several languages and was trained in the medical and chemical sciences of his time. Hahnemann's contribution to science was the development of a rigorous and inductive method of research, whereby nothing was taken for granted unless proven by multiple trials and verified in clinical practice. The theoretical findings of his many years of experiments were recorded in a book called Organon of the Medical Art.
Homœopathy is based on a number of principles. The first, 'like cures like', if developed further, leads to the principle of individualisation. By closely matching the entire diseased state of a person, including both objective and subjective symptoms, with a medicine, which has shown the ability to produce a similar state in a healthy individual, a homœopathic treatment will be most effective and lasting.
This foundation upon which homœopathy is based provides the premise, or required framework, for meaningful research into its efficacy. Current standards of scientific trials, which are based on statistic probabilities, do not sit comfortably with individualisation of medical treatment, rather, most medical trials are carried out to test the efficacy of a medical substance against the most common symptom/s of a given condition.
For example, medicines for asthma may be tested for their ability to dilate the airways, thereby relieving breathlessness, while not taking into account any other accompanying symptoms.
There is a growing body of research for homœopathy. Many trials have shown statistical efficacy even when using standard research methods as compared to the unique methodology required for homœopathic research.
The attached paper by R T Mathie discusses the research evidence base for homœopathy.
R T Mathie - Original Paper.
Below are some examples of homœopathic research for specific conditions.