Calligraphy is an ancient and diverse practice. Below are some resources I find useful:

Some contemporary calligraphers I like:

Ewan Clayton, Brody Neuenschwander, Denis Brown, Gareth Colgan, Mari Emily Bohley, Christopher Haanes

Some societies I like:

Society of Scribes and Illuminators, The Alcuin Society, Letter Exchange, Friends of Calligraphy

Some museums and archives I like:

The Klingspor Museum Offenback, The Harrison Collection,

The National Art Library V&A, St Bride Library

Ten (plus) books on calligraphy:

Donald Anderson The Art of Written Forms

John Howard Benson and Arthur Graham Carey The Elements of Lettering

George Bickham The Universal Penman

Hans-Joachim Burgert The Calligraphic Line translated by Brody Neuenschwander 

Ann Camp Pen Lettering

Edward M Catich The Origin of the Serif: Brush writing and Roman letters

Ewan Clayton The Golden Thread: The Story of Writing

Thomas James Cobden-Sanderson The Ideal Book or Book Beautiful

Alfred Faribank Italic Handwriting_

Gu Gan The Three Steps of Modern Calligraphy

André Gürtler Experiments with Letterform and Calligraphy

Christopher Haanes Calligraphy and Lettering

Edward Johnston Writing & Illuminating & Lettering

Abdelkebir Khatibi and Mohammed Sijelmassi The Splendor of Islamic Calligraphy

Rudolf Koch Das Schreiben als Kunstfertigkeit

John Neilson The Inscriptions of Ralph Beyer

Oscar Ogg Three Classics of Italian Calligraphy

Gottfried Pott Schrift, Klang, Bild

Ten (plus) books on typography:

Fernand Baudin How Typography Works: And Why it is Important

Robert Bringhurst The Elements of Typographic Style

William Addison Dwiggins Layout in Advertising

Eric Gill An Essay on Typography

Karl Gerstner Compendium for Literates

Armin Hofmann Graphic Design Manual: Principles and Practice

Robin Kinross Modern Typography

Josef Müller-Brockmann Grid Systems in Graphic Design

Paul Rand Thoughts on Design 

John Ryder Printing for Pleasure

Emil Ruder Typographie

Herbert Spencer Design in Business Printing

Jan Tschichold The New Typography

Jan Tschichold Penguin Composition Rules

Beatrice Warde The Chrystal Goblet 

Wolfgang Weingart My Way to Typography