Homeopathy is highly scientific, logical, safe, quick and extremely effective method of healing. It offers long lasting to permanent cure, treating the disease from its roots, for most of the ailments. Homeopathy does not treat superficially by just driving away the symptoms but heals the patient from within. Remember Hippocrates (The Father of Medicine, 460-377 B.C.). He said, "Natural forces within us are the true healers of disease".
How Homeopathy defines the health of an individual
Homeopathy is a most rational science with respect to its concepts of health, disease and cure. According to Homeopathy, health (and disease) is a dynamic entity. Signs of good health, apart from others, are mental clarity, emotional calm and refreshing sleep.
Health is not just merely an absence of disease but a state of equilibrium of the vital force that keeps the constitution of an individual in harmony.
Disease is not an entity. It is dynamic disposition (alteration) in harmony of constitution (due to dis-arrangement of vital force) not just the physio-chemical alteration of tissues.
Cure (-the single purpose and highest ideal of the medicine) is “the rapid, gentle and permanent restoration of health, or removal and annihilation of the disease in its whole extent, in the shortest, most reliable, and most harmless way, based on easily comprehensible principles” . Cure means the recovery of the state of stability of physiological norms .
“The Physician’s high and only mission is to restore the sick to health, to cure, as it is termed”
-Dr. Samuel Hahnemann, Aphorism 1, Organon of Rational Art of Healing, 1819
2. Preventive Medicine (1799)
Preventive use of homeopathy (called homeo-prophylaxis) was first applied in 1799 during an epidemic of scarlet fever in Königslütter, Germany, when Dr. Hahnemann prescribed a single dose of Belladona, as the remedy of the epidemic genius to susceptible children in the town with 100% success .
1896: Hueppe, a bacteriologist extended the findings to bacteria
Potentisation = Serial Dilution + Succussion
Succussion is a very specific and carefully controlled process in which there is agitation by vigorous shaking (10 to 150 damped strokes, boiron does 150 times in 7.5 seconds) or turbulent motion resulting in vibrations or molecular friction. Molecules contained in the drug substance gets liberated themselves from their inter-molecular bonds and get ionized. These ionized drug molecules thus attains a full expression of their chemical and biological properties, and become more virulent than the tightly packed original molecules. Latent energy (negatively charged) in the form of electro-magnetic pattern (negatively charged electro-magnetic energy) is released into the diluent/diluting liquid which become charged. Succussion is the amplification of that energy. Formative intelligence of the medicine is imprinted on the carrier (water-ethanol mixture). The diluent liquid then carries the energy.
Potentisation potentises (activates) the properties of the physical/remedy substance and transfers them to the solvent at the subtest energy level. The end result is refined and absolutely safe remedy that contains the 'dynamic curative power' of the crude drug substance. The potentised medicines influence the biochemical processes and relieve the pathological molecular inhibitions. This enables it to affect the body therapeutically. Potentisation increases the range and depth (more readily absorbed into the body tissues) of curative action of a drug.
The homeopathy potencies are prepared in three scales:
1. De-cimal (X or D)
2. Centi-cimal (C or CH),
3. Mille-cimal (LM or Q). LM potency is derived from 3C
These three scales are dilutions in multiple of 10, 100 and 50,0000 respectively.
Relationship between various scales dilution wise
2X = C (C is succussed more than X at same potency)
LM1 = 5.35 C (LM1 succussed considerably more than 6C)
LM3 = 10.35C (LM3 succussed considerably more than 12C)
LM30 = 63C (LM30 succussed considerably more than 30C)
7X is 10 times more diluted and 150 times more succussed than 6X.
The Potentisation problem
Video on How to prepare a remedy: Part-1 Part-II
1800: Hahnemann used Arsenicum in at least the 3C potency 
1801: In paper "Cure and prevention of scarlet fever", he mentioned the method to prepare potentised Belladonna
“we dissolve a grain of this powder ... in one hundred drops of common distilled water, by rubbing it up in a small mortar; we pour the thick solution into a one-ounce bottle, and rinse the mortar and the pestle with three hundred drops of diluted alcohol (five parts of water to one of spirit), and we then add this to the solution, and render the union perfect, by diligently shaking the liquid. We label the bottle strong solution of belladonna. One drop of this is intimately mixed with three hundred drops of diluted alcohol by shaking it for a minute, and this is marked medium solution of belladonna. Of this second mixture one drop is mixed with two hundred drops of the diluted alcohol, by shaking for a minute, and marked weak solution of belladonna; and this is our prophylactic remedy for scarlet-fever, each drop of which contains the twenty-four millionth part of a grain (0.0416 nanograms) of the dry belladonna juice.” (Lesser Writings, p. 380-381).
The concept of disease in homeopathy is that disease is a total affection of mind and body. Mind and body are dynamic and complex, with each part influencing the other and acting together. Neither mind nor body fall sick as separate units [7, pp.183]. Homeopathy is based on the fact that the person’s experience in emotional and mental (state of mind) life can not be separated from their physical complaints (body). Illness and physical problems can result in anxiety or emotional uneasiness. The opposite is also true. Most (not all) illnesses have their roots on mental plane. Very often mental troubles come first followed by physical complaints. Desire, anger, greed, pride, jealousy, suspicion, etc go on harassing and making our body also weaker and unable to resist diseases . Prolonged emotional stress can cause physical problems, like upset stomach, difficulty in digesting foods, poor nutrient assimilation, weaker immune system, sleeplessness, etc. Emotions are closely related to endocrine glands and nerves. The mind/emotions have real power to influence over the working of the physical body. That’s why homeopathy medicine is excellent for psycho-somatic diseases such as Migraine, Asthma, Peptic ulcer, Allergy, Ulcerative colitis, etc.
The medical maxim of Hippocrates and Plato is being followed in homeopathy. Hippocrates said, “It is more important to know the person who has the condition than it is to know the condition the person”. Plato said, "For the part can never be well, unless the whole is well".
1. Physical symptoms: Structure/built/looks, thermals such as tolerance to external factors like heat, cold, sun, wind, sound, light, peculiar symptoms such as inflammation without pain, etc Immunologists claim that the body has the capacity to “remember” every “assault” on the system that it has ever reacted to, and this process confirms that capacity .
2. Mental symptoms: state of mind, likes, dislikes, preferences, cravings, desires, aversions, thirst, appetite, temperament (reactions of mind to various external stimuli or circumstances)
3. Emotional Symptoms: Nature, behaviour, mood, emotions, sensitivity, reactions.
Constitution in homeopathy means a person’s state of health, including their temperament and any inherited and acquired characteristics. Environment (stress, shock, traumas producing changes in glands) modifies the constitution. When a homeopath physician during case taking takes all these above along with family history for prescribing a medicine, it becomes a genetic constitutional simillimum.
Individualisation: each person is unique/one size does not fit all.
Symptom X will always be cured by remedy Y no matter who the patient is. But no two patients can have same set of identical symptoms (physical+mental+emotional). Therefore two people suffering from the same disease are unlikely to be prescribed the same remedy and will come out to be different one. This is individualisation. No two individuals are alike in health or in disease. Thus homeopathy is not ready-made but tailor-made in terms of selection of remedy, potency (strength) and repetition to suit an individual. You can say homeopathy is a designer medicine.
6. Progress of cure in Chronic Diseases (The Chronic Diseases, 1828): It states that during the course of treatment the cure progresses from above (top of the body) downwards (bottom), from within outwards, center to periphery, from more important organ (wisdom of the body heals those most vital to life first) to less important one, in reverse order of coming of the symptoms (presenting symptoms disappear in the reverse order of their appearance i.e. First In Last Out, so old symptoms might resurface).
1845: Hering published in the preface of the first American edition of Hahnemann's Chronic Diseases an extract of an essay called "Guide to the Progressive Development of Homœopathy", a reference to the hahnemann's progress of cure.
1911: Kent in the first volume of the Transactions of the Society of Homœopathicians called "Correspondence of Organs, and the Direction of Cure" made a mistsake of reference of Hahnemann by Hering in 1945 as Hering's law.
More details here and here
To the list of Hahnemann, Dr. Praful Vijaykar adds a corollary: From more destructive miasm to less destructive i.e. from syphilis to sycosis to psora.
Immunologists claim that the body has the capacity to “remember” every “assault” on the system that it has ever reacted to, and this process confirms that capacity .