diff --git a/README.md b/README.md
index a04e56cb..c8895c0d 100644
--- a/README.md
+++ b/README.md
@@ -33,7 +33,7 @@ verification logic can be delayed to query and decision phase.
 - This implementation has low-degree test built-in, and can handle RS-IOP.
 - Multiple oracles with same evaluation domain share a merkle tree and be submitted in one round, which greatly reduces
   verification overhead and number of constraints.
-- Each leaf of an low-degree oracle is a coset instead of an individual field element, which significantly reduces
+- Each leaf of a low-degree oracle is a coset instead of an individual field element, which significantly reduces
   merkle tree overhead on FRI query.
  
 ## Build Guide
diff --git a/ark-bcs/src/bcs/constraints/verifier.rs b/ark-bcs/src/bcs/constraints/verifier.rs
index 402b3301..133f649a 100644
--- a/ark-bcs/src/bcs/constraints/verifier.rs
+++ b/ark-bcs/src/bcs/constraints/verifier.rs
@@ -237,7 +237,7 @@ where
 
     /// Verify without LDT.
     ///
-    /// ** Warning **: If verifier tries to get an low-degree oracle, no LDT
+    /// ** Warning **: If verifier tries to get a low-degree oracle, no LDT
     /// will be automatically performed.
     pub fn verify_with_dummy_ldt<V, S>(
         cs: ConstraintSystemRef<CF>,
diff --git a/ark-bcs/src/bcs/verifier.rs b/ark-bcs/src/bcs/verifier.rs
index 990c6456..ceb61fed 100644
--- a/ark-bcs/src/bcs/verifier.rs
+++ b/ark-bcs/src/bcs/verifier.rs
@@ -221,7 +221,7 @@ where
 
     /// Verify without LDT.
     ///
-    /// ** Warning **: If verifier tries to get an low-degree oracle, no LDT
+    /// ** Warning **: If verifier tries to get a low-degree oracle, no LDT
     /// will be automatically performed.
     pub fn verify_with_dummy_ldt<V, S>(
         sponge: S,
diff --git a/ark-bcs/src/iop/message.rs b/ark-bcs/src/iop/message.rs
index c2ef2007..c7ab5705 100644
--- a/ark-bcs/src/iop/message.rs
+++ b/ark-bcs/src/iop/message.rs
@@ -18,7 +18,7 @@ use super::{
 pub struct MsgRoundRef {
     pub(crate) index: usize,
     pub(crate) trace: TraceInfo,
-    /// Whether this round refers to an virtual oracle.
+    /// Whether this round refers to a virtual oracle.
     pub(crate) is_virtual: bool,
 }
 
diff --git a/ark-bcs/src/iop/mod.rs b/ark-bcs/src/iop/mod.rs
index a210280e..aae4c7dc 100644
--- a/ark-bcs/src/iop/mod.rs
+++ b/ark-bcs/src/iop/mod.rs
@@ -16,7 +16,7 @@ pub mod verifier;
 /// Prover parameter used by IOP Prover. Any IOP prover parameter is a superset
 /// of IOP verifier parameter.
 pub trait ProverParam: Clone + Debug {
-    /// Verifier state should be a improper subset of `self`.
+    /// Verifier state should be an improper subset of `self`.
     type VerifierParameter: VerifierParam;
     /// Derive verifier parameter from prover parameter.
     fn to_verifier_param(&self) -> Self::VerifierParameter;
diff --git a/ark-bcs/src/ldt/constraints/rl_ldt.rs b/ark-bcs/src/ldt/constraints/rl_ldt.rs
index 62854de0..ad40b8e7 100644
--- a/ark-bcs/src/ldt/constraints/rl_ldt.rs
+++ b/ark-bcs/src/ldt/constraints/rl_ldt.rs
@@ -241,7 +241,7 @@ impl<F: PrimeField + Absorb> LDTWithGadget<F> for LinearCombinationLDT<F> {
 
 /// return evaluation of x^{degree_to_raise} at specific location (with coset
 /// structure) For now, we assume the offset of codeword domain is constant.
-/// TODO: in the future, the offset can also be an variable.
+/// TODO: in the future, the offset can also be a variable.
 fn degree_raise_poly_query<F: PrimeField>(
     domain: Radix2CosetDomain<F>,
     degree_to_raise: u64,
diff --git a/ark-bcs/src/ldt/mod.rs b/ark-bcs/src/ldt/mod.rs
index 2a5bbfd9..7305314c 100644
--- a/ark-bcs/src/ldt/mod.rs
+++ b/ark-bcs/src/ldt/mod.rs
@@ -21,7 +21,7 @@ pub mod constraints;
 /// LDT that runs FRI on a random linear combination.
 pub mod rl_ldt;
 
-/// Trait for LDT, which is an public coin IOP.
+/// Trait for LDT, which is a public coin IOP.
 pub trait LDT<F: PrimeField + Absorb> {
     /// Parameters of `Self`
     type LDTParameters: Clone;