It is slightly more difficult to recommend resources that serve as concise, simple introductions to Lutheranism than it is to recommend resources introducing Christianity.
Partially, this is because the core resource for Lutheranism, The Book of Concord: The Confessions of the Evangelical Lutheran Church isn't widely known or read among Lutherans. Not only that, but many of the faith
commitments of the confessions, though ostensibly still commitments of contemporary Lutherans, are expressed in modes from which there has been considerable drift over the intervening 500 years.
Nevertheless, the confessions are a good place to start, so I recommend them.
Aside from the confessions, I highly recommend the web site of the ELCA, in particular the resources on ELCA Faith. This page includes click through resources to the Journal of Lutheran Ethics, inter-religious resources, basic introductions to Lutheran theology, and daily bible reading resources.
However, to get a sense of what it means to be a Lutheran today, I tend to think it is worth reading the stories of Lutherans. Some of the best include Richard Lischer's book on rural ministry, Open Secrets: A Memoir of Faith and Discovery, Nadia Bolz-Weber's memoir developing a congregation in urban Denver, Pastrix: The Cranky, Beautiful Faith of a Sinner & Saint, and Heidi Neumark's book on developing multicultural Lutheran ministries in the Bronx, Breathing Space: A Spiritual Journey in the South Bronx.
In my neck of the woods, I often end up needing to articulate the difference between different types of Lutheran, especially between the Missouri Synod and the ELCA. My basic answer is that the Missouri synod practices faith more out of the fundamentalist tradition, and so more conservative in terms of social norms--only male clergy, close communion, etc.--while ELCA practices faith more out of the liberal Protestant tradition--female clergy, openness to congregations calling clergy in same-gender marriages, etc.--while we also share many commitments, such as being liturgical in worship, and focused on social justice in the world, especially through ministries like Lutheran World Relief and Lutheran Immigration and Refugee Service.
For a great book that helps chart the emergence of the Missouri Synod as it distinguished itself increasingly from the merger Lutheran denominations, see Power Politics and the Missouri Synod
Another way to introduce Lutheranism is to simply point people to our core resources. Adults who participate in our catechumenate each year receive a copy of the Lutheran Study Bible and Evangelical Lutheran Worship: Pew Edition, our hymnal. Since Lutherans are above all people of Word & Sacrament, it makes sense for us to introduce Lutheranism by reading Scripture, and gathering for worship. That, better than anything else, gives indication of what Lutheranism is.
Some readers will really want to go deeper, delving either into the history or the theology of Lutheranism. For the history, I recommend A History of Lutheranism "Second Edition"
by Eric Gritsch.
For the theology, I recommend either Transformative Lutheran Theologies: Feminist, Womanist, and Mujerista Perspectives or Oswald Bayer's Theology the Lutheran Way (Lutheran Quarterly Books). Neither of these will be an easy read, but they will give a wide and comprehensive sense of what is particular, and peculiar, about Lutheranism in the 21st century.
Finally, it's worth recognizing that Lutheranism is a global movement. Some of the best resources for learning about Lutheranism in global perspective include the Lutheran World Federation web site, and The Future of Lutheranism in a Global Context, and Liberating Lutheran Theology: Freedom for Justice and Solidarity in a Global Context (Studies in Lutheran History and Theology).
To order the long-sleeve t-shirt at the top of the page, visit here. Old Lutheran rules.