tutorial: make titles clearer (I hope)

doc/source/tutorial/index.rst

-Tutorial: Learning Kwant through examples
+Tutorial: learning Kwant through examples
 =========================================
 
 .. toctree::

doc/source/tutorial/spin_orbit.py

@@ -38,14 +38,14 @@ def make_system(a=1, t=1.0, alpha=0.5, e_z=0.08, W=10, L=30):
 
     #### Define the scattering region. ####
 #HIDDEN_BEGIN_uxrm
-    sys[(lat(x, y) for x in range(L) for y in range(W))] = 4 * t * sigma_0 + \
-        e_z * sigma_z
+    sys[(lat(x, y) for x in range(L) for y in range(W))] = \
+        4 * t * sigma_0 + e_z * sigma_z
     # hoppings in x-direction
-    sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = -t * sigma_0 - \
-        1j * alpha * sigma_y
+    sys[kwant.builder.HoppingKind((1, 0), lat, lat)] = \
+        -t * sigma_0 - 1j * alpha * sigma_y
     # hoppings in y-directions
-    sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = -t * sigma_0 + \
-        1j * alpha * sigma_x
+    sys[kwant.builder.HoppingKind((0, 1), lat, lat)] = \
+        -t * sigma_0 + 1j * alpha * sigma_x
 #HIDDEN_END_uxrm
 
     #### Define the left lead. ####
@@ -54,11 +54,11 @@ def make_system(a=1, t=1.0, alpha=0.5, e_z=0.08, W=10, L=30):
 #HIDDEN_BEGIN_yliu
     lead[(lat(0, j) for j in xrange(W))] = 4 * t * sigma_0 + e_z * sigma_z
     # hoppings in x-direction
-    lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = -t * sigma_0 - \
-        1j * alpha * sigma_y
+    lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \
+        -t * sigma_0 - 1j * alpha * sigma_y
     # hoppings in y-directions
-    lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = -t * sigma_0 + \
-        1j * alpha * sigma_x
+    lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \
+        -t * sigma_0 + 1j * alpha * sigma_x
 #HIDDEN_END_yliu
 
     #### Attach the leads and return the finalized system. ####

doc/source/tutorial/tutorial1.rst

-First steps in Kwant: Setting up a simple system and computing transport
-------------------------------------------------------------------------
+First steps: setting up a simple system and computing conductance
+-----------------------------------------------------------------
 
 Discretization of a Schrödinger Hamiltonian
 ...........................................
@@ -321,20 +321,19 @@ subbands that increases with energy.
 .. [#] http://xkcd.com/353/
 .. [#] Leads are numbered in the python convention, starting from 0.
 
-The same but different: Alternative system building
-...................................................
+Building the same system with less code
+.......................................
 
-Kwant is very flexible, and often allows you more than one way to
-build up your system. The reason is that `~kwant.builder.Builder`
-is essentially just a container, and allows for different
-ways to be filled. Here we present a more compact rewrite of
-the previous example (still with the same results).
+Kwant allows for more than one way to build a system. The reason is that
+`~kwant.builder.Builder` is essentially just a container that can be filled in
+different ways. Here we present a more compact rewrite of the previous example
+(still with the same results).
 
-Also, the previous example was written in the form of a pythons script
-with little structure, and everything governed by global variables.
-This is OK for such a simple example, but for larger projects it makes
-sense to structure different functionality into different functional
-entities. In this example we therefore also aim at more structure.
+Also, the previous example was written in the form of a Python script with
+little structure, and with everything governed by global variables.  This is OK
+for such a simple example, but for larger projects it makes sense to partition
+the code into separate entities. In this example we therefore also aim at more
+structure.
 
 We begin the program collecting all imports in the beginning of the
 file and put the build-up of the system into a separate function

doc/source/tutorial/tutorial2.rst

-Adding more structure to the problem
-------------------------------------
+More interesting systems: spin, potential, shape
+------------------------------------------------
+
+Each of the following three examples highlights different ways to go beyond the
+very simple examples of the previous section.
 
 .. _tutorial_spinorbit:
 
 Matrix structure of on-site and hopping elements
 ................................................
 
-In the next examples, we will extend the previous examples and add more
-structure. We begin by extending the simple 2DEG-Hamiltonian by
-a Rashba spin-orbit coupling and a Zeeman splitting due to
-an external magnetic field:
+We begin by extending the simple 2DEG-Hamiltonian by a Rashba spin-orbit
+coupling and a Zeeman splitting due to an external magnetic field:
 
 .. math::
 

doc/source/tutorial/tutorial3.rst

-Beyond transport: Band structures and closed systems
-----------------------------------------------------
+Beyond transport: Band structure and closed systems
+---------------------------------------------------
 
 Band structure calculations
 ...........................

doc/source/tutorial/tutorial4.rst

 .. _tutorial-graphene:
 
-Using a more complicated lattice (graphene)
--------------------------------------------
+Beyond square lattices: graphene
+--------------------------------
 
 In the following example, we are going to calculate the
 conductance through a graphene quantum dot with a p-n junction

doc/source/tutorial/tutorial5.rst

-Superconductors: orbital vs lattice degrees of freedom
-------------------------------------------------------
+Superconductors: orbital vs. lattice degrees of freedom
+-------------------------------------------------------
 
 This example deals with superconductivity on the level of the
 Bogoliubov-de Gennes (BdG) equation. In this framework, the Hamiltonian
@@ -21,7 +21,7 @@ For this we restrict ourselves to a simple spin-less system without
 magnetic field, so that :math:`\Delta` is just a number (which we
 choose real), and :math:`\mathcal{T}H\mathcal{T}^{-1}=H_0^*=H_0`.
 
-"Orbital description": Using matrices
+"Orbital description": using matrices
 .....................................
 
 We begin by computing the band structure of a superconducting wire.
@@ -48,7 +48,7 @@ he?
     :download:`tutorial/superconductor_band_structure.py <../../../tutorial/superconductor_band_structure.py>`
 
 
-"Lattice description": Using different lattices
+"Lattice description": using different lattices
 ...............................................
 
 While it seems most natural to implement the BdG Hamiltonian