diff --git a/doc/tutorial/basics/imports.md b/doc/tutorial/basics/imports.md
index a05dce3..c6fdf59 100644
--- a/doc/tutorial/basics/imports.md
+++ b/doc/tutorial/basics/imports.md
@@ -3,7 +3,7 @@
 # Imports
 
 A CUE file may import definitions from builtin or user-defined packages.
-The CUE file itself does not need to be part of a package to use imports.
+A CUE file does not need to be part of a package to use imports.
 
 The example here shows the use of builtin packages.
 
diff --git a/doc/tutorial/basics/lists.md b/doc/tutorial/basics/lists.md
index 9d5f55b..f70dc1c 100644
--- a/doc/tutorial/basics/lists.md
+++ b/doc/tutorial/basics/lists.md
@@ -4,19 +4,19 @@
 
 Lists define arbitrary sequences of CUE values.
 A list can be closed or open ended.
-Open-ended lists may have some predefined elements, but may have number of
+Open-ended lists may have some predefined elements, but may have
 additional, possibly typed elements.
 
 In the example we define `IP` to be a list of `4` elements of type `uint8`, which
 is a predeclared value of `0..255`.
 `PrivateIP` defines the IP ranges defined for private use.
 Note that as it is already defined to be an `IP`, the length of the list
-is already fixed at `4` and we do not have to specify all elements.
+is already fixed at `4` and we do not have to specify a value for all elements.
 Also note that instead of writing `...uint8`, we could have written `...`
 as the type constraint is already already implied by `IP`.
 
-The output contains a valid private IP addresses `myIP`, and an invalid
-one `yourIP`.
+The output contains a valid private IP address (`myIP`)
+and an invalid one (`yourIP`).
 
 <!-- CUE editor -->
 ```
diff --git a/doc/tutorial/basics/operators.md b/doc/tutorial/basics/operators.md
index bb09a3b..f8ff10e 100644
--- a/doc/tutorial/basics/operators.md
+++ b/doc/tutorial/basics/operators.md
@@ -5,7 +5,8 @@
 CUE supports many common arithmetic and boolean operators.
 
 The operators for division and remainder are different for `int` and `float`.
-CUE supports both Euclidean division (`div` and `mod`)
+For `float` CUE supports the `/` and `%`  operators with the usual meaning.
+For `int` CUE supports both Euclidean division (`div` and `mod`)
 and truncated division (`quo` and `rem`).
 
 <!-- CUE editor -->
diff --git a/doc/tutorial/basics/packages.md b/doc/tutorial/basics/packages.md
index a61800d..f3a935e 100644
--- a/doc/tutorial/basics/packages.md
+++ b/doc/tutorial/basics/packages.md
@@ -7,7 +7,7 @@
 files.
 
 The configuration for a package is defined by the concatenation of all its
-files, after stripping the package clauses and not considering imports for now.
+files, after stripping the package clauses and not considering imports.
 
 Duplicate definitions are treated analogously to duplicate definitions within
 the same file.
diff --git a/doc/tutorial/basics/rangedef.md b/doc/tutorial/basics/rangedef.md
index 6bb34eb..31f7ce8 100644
--- a/doc/tutorial/basics/rangedef.md
+++ b/doc/tutorial/basics/rangedef.md
@@ -2,7 +2,7 @@
 
 # Predefined Ranges
 
-Numbers if CUE have arbitrary precision.
+CUE numbers have arbitrary precision.
 Also there is no unsigned integer type.
 
 CUE defines the following predefined identifiers to restrict the ranges of
diff --git a/doc/tutorial/basics/stringlit.md b/doc/tutorial/basics/stringlit.md
index 65a78e9..f5411e0 100644
--- a/doc/tutorial/basics/stringlit.md
+++ b/doc/tutorial/basics/stringlit.md
@@ -2,7 +2,7 @@
 
 # String Literals
 
-CUE stings allow a richer set of escape sequences.
+CUE strings allow a richer set of escape sequences than JSON.
 
 CUE also supports multi-line strings, enclosed by a pair of triple quotes `"""`.
 The opening quote must be followed by a newline.
diff --git a/doc/tutorial/basics/types.md b/doc/tutorial/basics/types.md
index baea3ca..bd8d06c 100644
--- a/doc/tutorial/basics/types.md
+++ b/doc/tutorial/basics/types.md
@@ -45,8 +45,7 @@
 yaxis: point
 yaxis y: 0
 
-origin: xaxis
-origin: yaxis
+origin: xaxis & yaxis
 ```
 
 <!-- result -->
@@ -55,17 +54,14 @@
     x: float
     y: float
 }
-
 xaxis: {
     x: 0
     y: float
 }
-
 yaxis: {
     x: float
     y: 0
 }
-
 origin: {
     x: 0
     y: 0
diff --git a/doc/tutorial/basics/unification.md b/doc/tutorial/basics/unification.md
index eb659e6..07cc11d 100644
--- a/doc/tutorial/basics/unification.md
+++ b/doc/tutorial/basics/unification.md
@@ -6,7 +6,7 @@
 This process is called unification.
 Unification can also be written explicitly with the `&` operator.
 
-There is always a single result, possibly bottom,
+There is always a single unique result, possibly bottom,
 for unifying any two CUE values.
 
 Unification is commutative, associative, and idempotent.