|Style over substance|
Graphology or handwriting analysis is the pseudoscientific idea that it is possible to assess someone's personality by analyzing their handwriting.
Claims include making judgments about a person's personality by looking at their handwriting, or even diagnosing disease. One typical claim is that the handwriting of introverts tilts to the left, and that of extroverts tilts to the right. Other claims include that you can detect whether a person is telling the truth by looking for specific indentations in their letters, or whether a person has a romantic interest in you by how large the loops on their "P"s and "R"s are. No scientific studies support any of these claims. Nonetheless, you can find several books purporting to tell you all about the subject in the New Age section of your local bookstore, but then again mentioning this is probably redundant.
 Legitimate uses
Handwriting analysis (also called graphanalysis) can also refer to the legitimate forensic investigation technique used by law enforcement, to determine whether handwriting found on an incriminating note or letter matches that of a suspect, based on expert scientific or technical knowledge of things ranging from types of paper and ink on handwriting, to knowledge of variation on handwriting due to fatigue, stress, and other factors, as well as a basic understanding of modern reproduction techniques. This has nothing to do with the woo mentioned above.
 Graphology and the scientific method
Graphology itself does not follow the scientific method. Graphologists observe patterns in peoples handwriting and create hypothesis to explain them, but often fail to make falsifiable and specific claims or do but leave themselves escape hatches (e.g. "Graphology is not accurate all the time. Behavior and personality change continuously. So taking handwriting samples for analysis over many months will give more information about the personality traits"). They then make predictions based on these hypotheses which is where scientists (from outside the graphologist communities) get involved and conduct double blind studies which quite consistently show graphologists do not make accurate predictions, often finding that their results are no better than guesswork or what could be ascertained from the content of the writing sample. These studies are as close as you will get to graphology experiments. Reproducibility is also difficult as there are various competing schools and theories about graphology (e.g. graphoanalysis, gestalt, or symbolic analysis), which do not validate or criticise each other to create a consensus, and cannot replicate one another's experiments as their methods are so different. Graphologists have created their own journals as mainstream peer reviewed journals will not usually accept their work.
Graphologists frequently point to anecdotal evidence and testimonials by people who feel their assessment is accurate, however this does not constitute scientific evidence owing to the possibility of cold reading tricks and the Dr Fox effect. Also, graphology is often meant to have indicated personality traits, such as introversion and extroversion which should be determined by a third party. If you have already been told by a graphologist that you're an introvert, then if you then complete a psychological questionnaire to determine if it's true, it'd be easy to (even unintentionally) give answers that fit what you have already been told. Controlled studies are intended to avoid these kinds of effects, and as stated, they do not support the claims of graphologists.
Graphotherapy is the process by which you change your handwriting to a writing that your chosen school of graphology would interpret positively, in the hope of acquiring the positive attributes they associate with it, such as optimism. This has a similar status to the rest of graphology in terms of a lack of controlled studies for evidence.